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2012-03-21
Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves
We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS with constant coefficients. The transformation is valid as long as |{\Gamma}t| \ll 1, with {\Gamma} the growth/damping rate of the waves due to the wind/dissipation. Approximate rogue wave solutions of the equation are presented and discussed. The results shed some lights on the effects of wind and dissipation on the formation of rogue waves.
1203.4735v1
2012-04-02
Random Symmetry Breaking and Freezing in Chaotic Networks
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped oscillators is shown to present chaotic dynamics while the amplitude sign of each damped oscillator is randomly frozen. This phenomenon of random broken global symmetry of the network simultaneously with random freezing of each degree of freedom is accompanied by the existence of exponentially many randomly frozen chaotic attractors with the ize of the network. Results are exemplified by a network of modified Duffing oscillators with infinite ange pseudo-inverse delayed interactions.
1204.0528v1
2012-04-04
Nonlinear Damping in Graphene Resonators
Based on a continuum mechanical model for single-layer graphene we propose and analyze a microscopic mechanism for dissipation in nanoelectromechanical graphene resonators. We find that coupling between flexural modes and in-plane phonons leads to linear and nonlinear damping of out-of-plane vibrations. By tuning external parameters such as bias and ac voltages, one can cross over from a linear to a nonlinear-damping dominated regime. We discuss the behavior of the effective quality factor in this context.
1204.0911v2
2012-05-22
Heavy quark damping rate in hot viscous QCD plasma
We derive an expression for the heavy quark damping rate in hot quark gluon plasma in presence of flow. Here all the bath particles here are out of equilibrium due to the existence of non-zero velocity gradient. The magnetic sector shows similar infrared divergences even after hard thermal loop corrections as one encounters in case of non-viscous plasma. We estimate the first order correction in ($\eta/s$) for heavy quark damping rate due to the non-zero viscosity of the QCD plasma.
1205.4895v3
2012-07-24
Quantum capacity of an amplitude-damping channel with memory
We calculate the quantum capacity of an amplitude-damping channel with time correlated Markov noise, for two channel uses. Our results show that memory of the channel increases it's ability to transmit quantum information significantly. We analyze and compare our findings with earlier numerical results on amplitude-damping channel with memory. An upper bound on the amount of quantum information transmitted over the channel in presence of memory, for an arbitrary number of channel uses is also presented.
1207.5612v3
2012-08-21
Protecting quantum entanglement from amplitude damping
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
1208.4187v2
2012-10-03
Exact solutions for discrete breathers in forced-damped chain
Exact solutions for symmetric discrete breathers (DBs) are obtained in forced-damped linear chain with on-site vibro-impact constraints. The damping is related to inelastic impacts; the forcing may be chosen from broad class of periodic antisymmetric functions. Global conditions for existence and stability of the DB are established. Some unusual phenomena, like non-monotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the full system and illustrated numerically for small periodic lattices.
1210.1085v1
2012-12-18
Using the mobile phone acceleration sensor in Physics experiments: free and damped harmonic oscillations
The mobile acceleration sensor has been used to in Physics experiments on free and damped oscillations. Results for the period, frequency, spring constant and damping constant match very well to measurements obtained by other methods. The Accelerometer Monitor application for Android has been used to get the outputs of the sensor. Perspectives for the Physics laboratory have also been discussed.
1212.4403v1
2012-12-20
How long-range interactions tune the damping in compact stars
Long-range interactions lead to non-Fermi liquid effects in dense matter. We show that, in contrast to other material properties, their effect on the bulk viscosity of quark matter is significant since they shift its resonant maximum and can thereby change the viscosity by many orders of magnitude. This is of importance for the damping of oscillations of compact stars, like in particular unstable r-modes, and the quest to detect signatures of deconfined matter in astrophysical observations. We find that, in contrast to neutron stars with standard damping mechanisms, compact stars that contain ungapped quark matter are consistent with the observed data on low mass x-ray binaries.
1212.5242v1
2013-02-12
Impact of gluon damping on heavy-quark quenching
In this conference contribution, we discuss the influence of gluon-bremsstrahlung damping in hot, absorptive QCD matter on the heavy-quark radiation spectra. Within our Monte-Carlo implementation for the description of the heavy-quark in-medium propagation we demonstrate that as a consequence of gluon damping the quenching of heavy quarks becomes significantly affected at higher transverse momenta.
1302.2934v1
2013-03-12
On nonlinear Schrodinger type equations with nonlinear damping
We consider equations of nonlinear Schrodinger type augmented by nonlinear damping terms. We show that nonlinear damping prevents finite time blow-up in several situations, which we describe. We also prove that the presence of a quadratic confinement in all spatial directions drives the solution of our model to zero for large time. In the case without external potential we prove that the solution may not go to zero for large time due to (non-trivial) scattering.
1303.3033v2
2013-06-15
A formula for damping interarea oscillations with generator redispatch
We derive a new formula for the sensitivity of electromechanical oscillation damping with respect to generator redispatch. The formula could lead to some combination of observations, computations and heuristics to more effectively damp interarea oscillations.
1306.3590v2
2013-07-24
Eigenvalue asymptotics for the damped wave equation on metric graphs
We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show that there is only a finite number of high-frequency abscissas, whose location is solely determined by the averages of the damping terms on each edge. We further describe some of the possible behaviour when the edge lengths are no longer necessarily equal but remain commensurate.
1307.6377v3
2013-08-03
Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping
Presented here is a study of a viscoelastic wave equation with supercritical source and damping terms. We employ the theory of monotone operators and nonlinear semigroups, combined with energy methods to establish the existence of a unique local weak solution. In addition, it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense.
1308.0720v2
2013-10-14
Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators
The damping rates of high quality factor nanomechanical resonators are well beyond intrinsic limits. Here, we explore the underlying microscopic loss mechanisms by investigating the temperature-dependent damping of the fundamental and third harmonic transverse flexural mode of a doubly clamped silicon nitride string. It exhibits characteristic maxima reminiscent of two-level defects typical for amorphous materials. Coupling to those defects relaxes the momentum selection rules, allowing energy transfer from discrete long wavelength resonator modes to the high frequency phonon environment.
1310.3671v1
2013-10-25
Quenched decoherence in qubit dynamics due to strong amplitude-damping noise
We study non-perturbatively the time evolution of a qubit subject to amplitude-damping noise. We show that at strong coupling the qubit decoherence can be quenched owing to large environment feedbacks, such that the qubit can evolve coherently even in the long-time limit. As an application, we show that for a quantum channel that consists of two independent qubits subject to uncorrelated local amplitude-damping noises, it can maintain at strong coupling finite entanglement and better than classical teleportation fidelity at long times.
1310.6843v2
2013-11-16
Shear viscosity due to the Landau damping from quark-pion interaction
We have calculated the shear viscosity coefficient $\eta$ of the strongly interacting matter in the relaxation time approximation, where a quasi particle description of quarks with its dynamical mass is considered from NJL model. Due to the thermodynamic scattering of quarks with pseudo scalar type condensate (i.e. pion), a non zero Landau damping will be acquired by the propagating quarks. This Landau damping may be obtained from the Landau cut contribution of the in-medium self-energy of quark-pion loop, which is evaluated in the framework of real-time thermal field theory.
1311.4070v1
2013-12-19
Cyclotron dynamics of interacting bosons in artificial magnetic fields
We study theoretically quantum dynamics of interacting bosons in artificial magnetic fields as engineered in recent ultracold atomic experiments, where quantum cyclotron orbital motion has been observed. With exact numerical simulations and perturbative analyses, we find that interactions induce damping in the cyclotron motion. The damping time is found to be dependent on interaction and tunneling strengths monotonically, while its dependence on magnetic flux is non-monotonic. Sufficiently strong interactions would render bosons dynamically localized inhibiting the cyclotron motion. The damping predicted by us can be construed as an interaction-induced quantum decoherence of the cyclotron motion.
1312.5747v2
2014-01-11
Damping in two component Bose gas
We investigate the Landau and Baliaev damping of the collective modes in a two-component Bose gas using the mean-field approximation. We show that due to the two body atom-atom interaction, oscillations of each component is coupled to the thermal excitations of the other component which gives rise to creation or destruction of the elementary excitations that can take place in the two separate components.In addition we find that the damping is also enhanced due to inter-component coupling.
1401.2537v1
2014-03-24
Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations
In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations with pseudo-almost automorphic coefficients. In order to illustrate our main results, we will study the existence of pseudo-almost automorphic solutions to a structurally damped plate-like boundary value problem.
1403.5955v1
2014-04-25
The time singular limit for a fourth-order damped wave equation for MEMS
We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential. We first review some recent results on existence and non-existence of steady-states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit when the ratio between inertial and damping effects tends to zero.
1404.6342v1
2014-05-12
A note on a strongly damped wave equation with fast growing nonlinearities
A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the nonlinearities involved the initial boundary value problem for the considered equation is globally well-posed in the class of sufficiently regular solutions and the semigroup generated by the problem possesses a global attractor in the corresponding phase space. These results are obtained for the nonlinearities of an arbitrary polynomial growth and without the assumption that the considered problem has a global Lyapunov function.
1405.2707v1
2014-06-03
Optimal Estimation of a Classical Force with a Damped Oscillator in the non-Markovian Bath
We solve the optimal quantum limit of probing a classical force exactly by a damped oscillator initially prepared in the factorized squeezed state. The memory effects of the thermal bath on the oscillator evolution are investigated. We show that the optimal force sensitivity obtained by the quantum estimation theory approaches to zero for the non-Markovian bath, whereas approaches to a finite non-zero value for the Markovian bath as the energy of the damped oscillator goes to infinity.
1406.0658v1
2014-08-09
Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions
We investigate the Westervelt equation with several versions of nonlinear damping and lower order damping terms and Neumann as well as absorbing boundary conditions. We prove local in time existence of weak solutions under the assumption that the initial and boundary data are sufficiently small. Additionally, we prove local well-posedness in the case of spatially varying $L^{\infty}$ coefficients, a model relevant in high intensity focused ultrasound (HIFU) applications.
1408.2160v1
2014-08-11
Characterization and suppression techniques for degree of radiation damping in inversion recovery measurements
Radiation damping (RD) has been shown to affect T1 measurement in inversion recovery experiments. In this work, we demonstrate that the extent of RD depends upon the T1 of the sample. RD difference spectroscopy (RADDSY) is used to characterize the severity of RD, while gradient inversion recovery (GIR) is used for RD suppression in T1 measurements. At 9.4 T, for the radiation damping characteristic time (Trd) of 50 ms, these investigations show non-negligible RD effects for T1 values greater than Trd, with severe distortions for T1 longer than about 150 ms, showing reasonable agreement with the predicted Trd. We also report a discrepancy between published expressions for the characteristic RD time.
1408.2457v2
2014-09-28
Spin-electron acoustic waves: The Landau damping and ion contribution in the spectrum
Separated spin-up and spin-down quantum kinetics is derived for more detailed research of the spin-electron acoustic waves. Kinetic theory allows to obtain spectrum of the spin-electron acoustic waves including effects of occupation of quantum states more accurately than quantum hydrodynamics. We apply quantum kinetic to calculate the Landau damping of the spin-electron acoustic waves. We have considered contribution of ions dynamics in the spin-electron acoustic wave spectrum. We obtain contribution of ions in the Landau damping in temperature regime of classic ions. Kinetic analysis for ion-acoustic, zero sound, and Langmuir waves at separated spin-up and spin-down electron dynamics is presented as well.
1409.7885v1
2014-10-05
Ultimate limit of field confinement by surface plasmon polaritons
We show that electric field confinement in surface plasmon polaritons propagating at the metal/dielectric interfaces enhances the loss due to Landau damping and which effectively limits the degree of confinement itself. We prove that Landau damping and associated with it surface collision damping follow directly from Lindhard formula for the dielectric constant of free electron gas Furthermore, we demonstrate that even if all the conventional loss mechanisms, caused by phonons, electron-electron, and interface roughness scattering, were eliminated, the maximum attainable degree of confinement and the loss accompanying it would not change significantly compared to the best existing plasmonic materials, such as silver.
1410.1226v1
2014-10-15
Quasiparticle Damping of Surface Waves in Superfluid $^3$He and $^4$He
Oscillations on free surface of superfluids at the inviscid limit are damped by quasiparticle scattering. We have studied this effect in both superfluids $^3$He and $^4$He deep below the respective critical temperatures. Surface oscillators offer several benefits over immersed mechanical oscillators traditionally used for similar purposes. Damping is modeled as specular scattering of ballistic quasiparticles from the moving free surface. The model is in reasonable agreement with our measurements for superfluid $^4$He but significant deviation is found for $^3$He.
1410.4071v1
2014-12-22
Long time behavior for a semilinear hyperbolic equation with asymtotically vanishing damping term and convex potential
We investigate the asymptotic behavior, as t goes to infinity, for a semilinear hyperbolic equation with asymptotically smal dissipation and convex potential. We prove that if the damping term behaves like K/t^\alpha for t large enough, k>0 and 0</alpha<1 then every global solution converges weakly to an equilibrium point. This result is a positive answer to a question left open in the paper [A. Cabot and P. Frankel, Asymptotics for some semilinear hyperbolic equation with non-autonomous damping. J. Differential Equations 252 (2012) 294-322.]
1412.7008v1
2015-03-03
Large Deviations for the Langevin equation with strong damping
We study large deviations in the Langevin dynamics, with damping of order $\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then, we use a weak convergence approach to large deviations and their equivalent formulation in terms of the Laplace principle, to determine the good action functional. Some applications of these results to the exit problem from a domain and to the wave front propagation for a suitable class of reaction diffusion equations are considered.
1503.01027v1
2015-03-14
Stabilization of the nonlinear damped wave equation via linear weak observability
We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the corresponding undamped system. One of the main advantage of these results is that they allow to combine the optimal-weight convexity method of Alabau-Boussouira and a methodology of Ammari-Tucsnak for weak stabilization by observability. Our results extend to nonlinearly damped systems, those of Ammari and Tucsnak. At the end, we give an appendix on the weak stabilization of linear evolution systems.
1503.04356v1
2015-06-02
On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source
The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for initial data in the natural energy space. Moreover the regularity of solutions is studied. Finally a dynamical system is generated when sources are at most linear at infinity, or they are dominated by the damping terms.
1506.00910v4
2015-06-15
Tautochrone in the damped cycloidal pendulum
The tautochrone on a cycloid curve is usually considered without drag force. In this work, we investigate the motion of a damped cycloidal pendulum under presence of a drag force. Using the Lagrange formulation, and considering linear dependence with velocity for damping force, we found the dynamics of the system to remain tautochrone. This dictates the possibility for studying the tautochrone experimentally, e.g. the cycloidal pendulum in water or oil.
1506.04943v2
2015-07-04
Comments on turbulence theory by Qian and by Edwards and McComb
We reexamine Liouville equation based turbulence theories proposed by Qian {[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys. A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov spectrum. These theories obtained identical equation for spectral density $q(k)$ and different results for damping coefficient. Qian proposed variational approach and Edwards and McComb proposed maximal entropy principle to obtain equation for the damping coefficient. We show that assumptions used in these theories to obtain damping coefficient correspond to unphysical conditions.
1507.01124v1
2015-08-24
Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations, then the solution is approximated by the scaled Gaussian of the corresponding linear parabolic problem. The proof is based on the scaling variables and energy estimates.
1508.05778v3
2015-10-01
Impact of surface collisions on enhancement and quenching of the luminescence near the metal nanoparticles
The fact that surface-induced damping rate of surface plasmon polaritons (SPPs) in metal nanoparticles increases with the decrease of particle size is well known. We show that this rate also increases with the degree of the mode confinement, hence damping of the higher order nonradiative SPP modes in spherical particles is greatly enhanced relative to damping of the fundamental (dipole) SPP mode. Since higher order modes are the ones responsible for quenching of luminescence in the vicinity of metal surfaces, the degree of quenching increases resulting in a substantial decrease in the amount of attainable enhancement of the luminescence
1510.00321v1
2015-10-22
On numerical Landau damping for splitting methods applied to the Vlasov-HMF model
We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field) equation based on splitting methods between the linear and non-linear parts. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that the numerical solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping. Moreover, we prove that the modified state is close to the continuous one and provide error estimates with respect to the time stepsize.
1510.06555v1
2015-11-02
Asymptotic decomposition for nonlinear damped Klein-Gordon equations
In this paper, we proved that if the solution to damped focusing Klein-Gordon equations is global forward in time, then it will decouple into a finite number of equilibrium points with different shifts from the origin. The core ingredient of our proof is the existence of the "concentration-compact attractor" which yields a finite number of profiles. Using damping effect, we can prove all the profiles are equilibrium points.
1511.00437v3
2015-11-11
Contact Stiffness and Damping of Liquid Films in Dynamic Atomic Force Microscopy
Small-amplitude dynamic atomic force microscopy (dynamic-AFM) in a simple nonpolar liquid was studied through molecular dynamics simulations. We find that within linear dynamics regime, the contact stiffness and damping of the confined film exhibit the similar solvation force oscillations, and they are generally out-of-phase. For the solidified film with integer monolayer thickness, further compression of the film before layering transition leads to higher stiffness and lower damping. We find that molecular diffusion in the solidified film was nevertheless enhanced due to the mechanical excitation of AFM tip.
1511.03580v1
2015-11-13
Nonlinear Radiation Damping of Nuclear Spin Waves and Magnetoelastic Waves in Antiferromagnets
Parallel pumping of nuclear spin waves in antiferromagnetic CsMnF3 at liquid helium temperatures and magnetoelastic waves in antiferromagnetic FeBO3 at liquid nitrogen temperature in a helical resonator was studied. It was found that the absorbed microwave power is approximately equal to the irradiated power from the sample and that the main restriction mechanism of absortption in both cases is defined by the nonlinear radiation damping predicted about two decades ago. We believe that the nonlinear radiation damping is a common feature of parallel pumping technique of all normal magnetic excitations and it can be detected by purposeful experiments.
1511.04396v1
2016-03-01
Damped vacuum states of light
We consider one-dimensional propagation of quantum light in the presence of a block of material, with a full account of dispersion and absorption. The electromagnetic zero-point energy for some frequencies is damped (suppressed) by the block below the free-space value, while for other frequencies it is increased. We also calculate the regularized (Casimir) zero-point energy at each frequency and find that it too is damped below the free-space value (zero) for some frequencies. The total Casimir energy is positive.
1603.00233v2
2016-04-18
Parameter Estimation of Gaussian-Damped Sinusoids from a Geometric Perspective
The five parameter gaussian damped sinusoid equation is a reasonable model for betatron motion with chromatic decoherence of the proton bunch centroid signal in the ring at the Spallation Neutron Source. A geometric method for efficiently fitting this equation to the turn by turn signals to extract the betatron tune and damping constant will be presented. This method separates the parameters into global and local parameters and allows the use of vector arithmetic to eliminate the local parameters from the parameter search space. Furthermore, this method is easily generalized to reduce the parameter search space for a larger class of problems.
1604.05167v1
2016-04-20
Landau damping in finite regularity for unconfined systems with screened interactions
We prove Landau damping for the collisionless Vlasov equation with a class of $L^1$ interaction potentials (including the physical case of screened Coulomb interactions) on $\mathbb R^3_x \times \mathbb R^3_v$ for localized disturbances of an infinite, homogeneous background. Unlike the confined case $\mathbb T^3_x \times \mathbb R_v^3$, results are obtained for initial data in Sobolev spaces (as well as Gevrey and analytic classes). For spatial frequencies bounded away from zero, the Landau damping of the density is similar to the confined case. The finite regularity is possible due to an additional dispersive mechanism available on $\mathbb R_x^3$ which reduces the strength of the plasma echo resonance.
1604.05783v1
2016-04-26
Trigonometric Splines for Oscillator Simulation
We investigate the effects of numerical damping for oscillator simulation with spline methods. Numerical damping results in an artificial loss of energy and leads therefore to unreliable results in the simulation of autonomous systems, as e.g.\ oscillators. We show that the negative effects of numerical damping can be eliminated by the use of trigonometric splines. This will be in particular important for spline based adaptive methods.
1604.07607v1
2016-07-13
Optimal decay rate for the wave equation on a square with constant damping on a strip
We consider the damped wave equation with Dirichlet boundary conditions on the unit square. We assume the damping to be a characteristic function of a strip. We prove the exact $t^{-4/3}$-decay rate for the energy of classical solutions. This answers a question of Anantharaman and L\'eautaud (2014).
1607.03633v2
2016-08-29
Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles
In this paper, by using classical Faedo-Galerkin approximation and compactness method, the existence of martingale solutions for the stochastic 3D Navier-Stokes equations with nonlinear damping is obtained. The existence and uniqueness of strong solution are proved for $\beta > 3$ with any $\alpha>0$ and $\alpha \geq \frac12$ as $\beta = 3$. Meanwhile, a small time large deviation principle for the stochastic 3D Navier-Stokes equation with damping is proved for $\beta > 3$ with any $\alpha>0$ and $\alpha \geq \frac12$ as $\beta = 3$.
1608.07996v1
2016-09-05
Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity
We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.
1609.01035v2
2016-09-06
Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping
This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate of classical solutions of the p-system with damping towards the smooth solutions of the porous media equation using a relative entropy method. Adopting a semi-discrete scheme, we establish that the convergence rate is preserved by the approximated solutions. Several numerical experiments illustrate the relevance of this result.
1609.01436v1
2016-09-20
Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent damping
We study the isentropic Euler equations with time-dependent damping, given by $\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative constants to describe the decay rate of damping with respect to time. We will investigate the global existence and asymptotic behavior of small data solutions to the Euler equations when $0<\lambda<1,0<\mu$ in multi-dimensions $n\geq 1$. The asymptotic behavior will coincide with the one that obtained by many authors in the case $\lambda=0$. We will also show that the solution can only decay polynomially in time while in the three dimensions, the vorticity will decay exponentially fast.
1609.06286v1
2016-11-08
Emulated Inertia and Damping of Converter-Interfaced Power Source
Converter-interfaced power sources (CIPSs), like wind turbine and energy storage, can be switched to the inertia emulation mode when the detected frequency deviation exceeds a pre-designed threshold, i.e. dead band, to support the frequency response of a power grid. This letter proposes an approach to derive the emulated inertia and damping from a CIPS based on the linearized model of the CIPS and the power grid, where the grid is represented by an equivalent single machine. The emulated inertia and damping can be explicitly expressed in time and turn out to be time-dependent.
1611.02698v1
2016-12-09
Ornstein-Uhlenbeck Process with Fluctuating Damping
This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the dichotomous noise and fractional Gaussian noise are considered. Their solutions are obtained explicitly, with the expressions of the mean and covariance determined explicitly. Properties of the mean and covariance of the Ornstein-Uhlenbeck process with random damping, in particular the asymptotic behavior, are studied. The effect of the multiplicative noise on the stability property of the resulting processes is investigated.
1612.03013v3
2016-12-20
Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment
We consider a nonlinear Timoshenko system of partial differential equations (PDEs) with a frictional damping term in rotation angle. The nonlinearity is due to the arbitrary dependence on the rotation moment. A Lie symmetry group classification of the arbitrary function of rotation moment is presented. An optimal system of one-dimensional subalgebras of the nonlinear damped Timoshenko system is derived for all the non-linear cases. All possible invariant variables of the optimal systems for the three non-linear cases are presented. The corresponding reduced systems of ordinary differential equations (ODEs) are also provided.
1612.06775v1
2017-03-14
Landau damping in the multiscale Vlasov theory
Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. The extended Vlasov equation keeps the reversibility, the Hamiltonian structure, and the entropy conservation of the original Vlasov equation. In the setting of the extended Vlasov theory we then argue that the Fokker-Planck type damping in the velocity dependence of the extra distribution function induces the Landau damping. The same type of extension is made also in the setting of fluid mechanics.
1703.04577v2
2017-03-15
Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation
We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly understood, this paper is mainly about the contribution of low frequencies. We show in particular that the damped wave behaves like a solution of a heat equation which depends on the H-limit of the metric and the mean value of the absorption index.
1703.05112v1
2017-04-03
Linear inviscid damping and vorticity depletion for shear flows
In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the explicit decay estimates of the velocity, which is the same as one for monotone shear flows. We confirm a new dynamical phenomena found by Bouchet and Morita: the depletion of the vorticity at the stationary streamlines, which could be viewed as a new mechanism leading to the damping for the base flows with stationary streamlines.
1704.00428v1
2017-04-25
Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity
In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat equation as time tends to infinity. The proof is based on semigroup estimates for the corresponding heat equation and weighted energy estimates for the damped wave equation. To construct a suitable weight function for the energy estimates, we study a certain elliptic problem.
1704.07650v1
2017-06-05
Mixed finite elements for global tide models with nonlinear damping
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy accumulation. We also give rates of damping in unforced systems and various continuous dependence results on initial conditions and forcing terms. \emph{A priori} error estimates for the momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.
1706.01352v1
2017-06-13
Uniform energy decay for wave equations with unbounded damping coefficients
We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solution, and we try to deal with an essential unbounded coefficient case.
1706.03942v1
2017-06-15
Fractional Driven Damped Oscillator
The resonances associated with a fractional damped oscillator which is driven by an oscillatory external force are studied. It is shown that such resonances can be manipulated by tuning up either the coefficient of the fractional damping or the order of the corresponding fractional derivatives.
1706.08596v1
2017-07-11
Stability of partially locked states in the Kuramoto model through Landau damping with Sobolev regularity
The Kuramoto model is a mean-field model for the synchronisation behaviour of oscillators, which exhibits Landau damping. In a recent work, the nonlinear stability of a class of spatially inhomogeneous stationary states was shown under the assumption of analytic regularity. This paper proves the nonlinear Landau damping under the assumption of Sobolev regularity. The weaker regularity required the construction of a different more robust bootstrap argument, which focuses on the nonlinear Volterra equation of the order parameter.
1707.03475v2
2017-08-27
Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case
We study global existence of solutions to the Cauchy problem for the wave equation with time-dependent damping and a power nonlinearity in the overdamping case. We prove the global well-posedness for small data in the energy space for the whole energy-subcritical case. This result implies that small data blow-up does not occur in the overdamping case, different from the other cases, i.e. effective or non-effective damping.
1708.08044v2
2017-09-04
A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent
We concern the blow up problem to the scale invariant damping wave equations with sub-Strauss exponent. This problem has been studied by Lai, Takamura and Wakasa (\cite{Lai17}) and Ikeda and Sobajima \cite{Ikedapre} recently. In present paper, we extend the blowup exponent from $p_F(n)\leq p<p_S(n+2\mu)$ to $1<p<p_S(n+\mu)$ without small restriction on $\mu$. Moreover, the upper bound of lifespan is derived with uniform estimate $T(\varepsilon)\leq C\varepsilon^{-2p(p-1)/\gamma(p,n+2\mu)}$. This result extends the blowup result of semilinear wave equation and shows the wave-like behavior of scale invariant damping wave equation's solution even with large $\mu>1$.
1709.00866v2
2017-09-13
Life-span of blowup solutions to semilinear wave equation with space-dependent critical damping
This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical space-dependent damping term (DW:$V$). The main result of the present paper is to give a solution of the problem and to provide a sharp estimate for lifespan for such a solution when $\frac{N}{N-1}<p\leq p_S(N+V_0)$, where $p_S(N)$ is the Strauss exponent for (DW:$0$). The main idea of the proof is due to the technique of test functions for (DW:$0$) originated by Zhou--Han (2014, MR3169791). Moreover, we find a new threshold value $V_0=\frac{(N-1)^2}{N+1}$ for the coefficient of critical and singular damping $|x|^{-1}$.
1709.04401v1
2017-09-24
Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations
We study the unphysical recurrence phenomenon arising in the numerical simulation of the transport equations using Hermite-spectral method. From a mathematical point of view, the suppression of this numerical artifact with filters is theoretically analyzed for two types of transport equations. It is rigorously proven that all the non-constant modes are damped exponentially by the filters in both models, and formally shown that the filter does not affect the damping rate of the electric energy in the linear Landau damping problem. Numerical tests are performed to show the effect of the filters.
1709.08194v1
2017-11-01
Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case
The blow up problem of the semilinear scale-invariant damping wave equation with critical Strauss type exponent is investigated. The life span is shown to be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for $0<\mu<\frac{n^2+n+2}{n+2}$. This result completes our previous study \cite{Tu-Lin} on the sub-Strauss type exponent $p<p_S(n+\mu)$. Our novelty is to construct the suitable test function from the modified Bessel function. This approach might be also applied to the other type damping wave equations.
1711.00223v1
2017-11-14
Spin-Noise and Damping in Individual Metallic Ferromagnetic Nanoparticles
We introduce a highly sensitive and relatively simple technique to observe magnetization motion in single Ni nanoparticles, based on charge sensing by electron tunneling at millikelvin temperature. Sequential electron tunneling via the nanoparticle drives nonequilibrium magnetization dynamics, which induces an effective charge noise that we measure in real time. In the free spin diffusion regime, where the electrons and magnetization are in detailed balance, we observe that magnetic damping time exhibits a peak with the magnetic field, with a record long damping time of $\simeq 10$~ms.
1711.05142v1
2017-12-04
Graviton-mediated dark matter model explanation the DAMPE electron excess and search at $e^+e^-$ colliders
The very recent result of the DAMPE cosmic ray spectrum of electrons shows a narrow bump above the background at around 1.4 TeV. We attempt to explain the DAMPE electron excess in a simplified Kaluza-Klein graviton-mediated dark matter model, in which the graviton only interacts with leptons and dark matter. The related phenomenological discussions are given and this simplified graviton-mediated dark matter model has the potential to be cross-tested in future lepton collider experiments.
1712.01143v1
2017-12-13
On nonlinear damped wave equations for positive operators. I. Discrete spectrum
In this paper we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to the linear problem with decay rate depending on the interplay between the bottom of the operator's spectrum and the mass term. Consequently, we prove global in time well-posedness results for semilinear and for more general nonlinear equations with small data. Examples are given for nonlinear damped wave equations for the harmonic oscillator, for the twisted Laplacian (Landau Hamiltonian), and for the Laplacians on compact manifolds.
1712.05009v1
2018-03-14
Damped Newton's Method on Riemannian Manifolds
A damped Newton's method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the proposed method reduces to a sequence generated by the Riemannian version of the classical Newton's method after a finite number of iterations, consequently its convergence rate is superlinear/quadratic. Moreover, numerical experiments illustrate that the damped Newton's method has better performance than Newton's method in number of iteration and computational time.
1803.05126v2
2018-05-29
Asymptotic profile of solutions for strongly damped Klein-Gordon equations
We consider the Cauchy problem in the whole space for strongly damped Klein-Gordon equations. We derive asymptotic profles of solutions with weighted initial data by a simple method introduced by R. Ikehata. The obtained results show that the wave effect will be weak because of the mass term, especially in the low dimensional case (n = 1,2) as compared with the strongly damped wave equations without mass term (m = 0), so the most interesting topic in this paper is the n = 1,2 cases.
1805.11975v1
2018-06-08
Brownian motion of magnetic domain walls and skyrmions, and their diffusion constants
Extended numerical simulations enable to ascertain the diffusive behavior at finite temperatures of chiral walls and skyrmions in ultra-thin model Co layers exhibiting symmetric - Heisenberg - as well as antisymmetric - Dzyaloshinskii-Moriya - exchange interactions. The Brownian motion of walls and skyrmions is shown to obey markedly different diffusion laws as a function of the damping parameter. Topology related skyrmion diffusion suppression with vanishing damping parameter, albeit already documented, is shown to be restricted to ultra-small skyrmion sizes or, equivalently, to ultra-low damping coefficients, possibly hampering observation.
1806.03172v1
2018-06-18
Damped second order flow applied to image denoising
In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the St\"{o}rmer-Verlet method, a discrete damped flow, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the feasibility and effectiveness of the SV-DDF.
1806.06732v2
2018-07-10
Cyclotron Damping along an Uniform Magnetic Field
We prove cyclotron damping for the collisionless Vlasov-Maxwell equations on $\mathbb{T}_{x}^{3}\times\mathbb{R}_{v}^{3}$ under the assumptions that the electric induction is zero and $(\mathcal{\mathbf{PSC}})$ holds. It is a crucial step to solve the stability problem of the Vlasov-Maxwell equations. Our proof is based on a new dynamical system of the plasma particles, originating from Faraday Law of Electromagnetic induction and Lenz's Law. On the basis of it, we use the improved Newton iteration scheme to show the damping mechanism.
1807.05254v3
2018-07-17
On the blow-up for critical semilinear wave equations with damping in the scattering case
We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in $\mathbf{R}^n$, where $n\geq 2$. It is expected that the critical exponent will be Strauss' number $p_0(n)$, which is also the one for semilinear wave equations without damping terms. Lai and Takamura (2018) have obtained the blow-up part, together with the upper bound of lifespan, in the sub-critical case $p<p_0(n)$. In this paper, we extend their results to the critical case $p=p_0(n)$. The proof is based on Wakasa and Yordanov (2018), which concerns the blow-up and upper bound of lifespan for critical semilinear wave equations with variable coefficients.
1807.06164v1
2018-08-22
Radiation Damping of a Yang-Mills Particle Revisited
The problem of a color-charged point particle interacting with a four dimensional Yang-Mills gauge theory is revisited. The radiation damping is obtained inspired in the Dirac's computation. The difficulties in the non-abelian case were solved by using an ansatz for the Li\'enard-Wiechert potentials, already used in the literature for finding solutions to the Yang-Mills equations. Three non-trivial examples of radiation damping for the non-abelian particle are discussed in detail.
1808.07533v2
2018-08-28
Enhancement of zonal flow damping due to resonant magnetic perturbations in the background of an equilibrium $E \times B$ sheared flow
Using a parametric interaction formalism, we show that the equilibrium sheared rotation can enhance the zonal flow damping effect found in Ref. [M. Leconte and P.H. Diamond, \emph{Phys. Plasmas} 19, 055903 (2012)]. This additional damping contribution is proportional to $(L_s/L_V)^2 \times \delta B_r^2 / B^2$, where $L_s/L_V$ is the ratio of magnetic shear length to the scale-length of equilibrium $E \times B$ flow shear, and $\delta B_r / B$ is the amplitude of the external magnetic perturbation normalized to the background magnetic field.
1808.09110v1
2018-08-30
Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities
In this paper, by means of the Riesz basis approach, we study the stability of a weakly damped system of two second order evolution equations coupled through the velocities. If the fractional order damping becomes viscous and the waves propagate with equal speeds, we prove exponential stability of the system and, otherwise, we establish an optimal polynomial decay rate. Finally, we provide some illustrative examples.
1808.10256v1
2018-09-10
Linear inviscid damping for the $β$-plane equation
In this paper, we study the linear inviscid damping for the linearized $\beta$-plane equation around shear flows. We develop a new method to give the explicit decay rate of the velocity for a class of monotone shear flows. This method is based on the space-time estimate and the vector field method in sprit of the wave equation. For general shear flows including the Sinus flow, we also prove the linear damping by establishing the limiting absorption principle, which is based on the compactness method introduced by Wei-Zhang-Zhao in \cite{WZZ2}. The main difficulty is that the Rayleigh-Kuo equation has more singular points due to the Coriolis effects so that the compactness argument becomes more involved and delicate.
1809.03065v1
2018-10-14
Critical exponent for nonlinear damped wave equations with non-negative potential in 3D
We are studying possible interaction of damping coefficients in the subprincipal part of the linear 3D wave equation and their impact on the critical exponent of the corresponding nonlinear Cauchy problem with small initial data. The main new phenomena is that certain relation between these coefficients may cause very strong jump of the critical Strauss exponent in 3D to the critical 5D Strauss exponent for the wave equation without damping coefficients.
1810.05956v1
2018-10-23
Perfect absorption of water waves by linear or nonlinear critical coupling
We report on experiments of perfect absorption for surface gravity waves impinging a wall structured by a subwavelength resonator. By tuning the geometry of the resonator, a balance is achieved between the radiation damping and the intrinsic viscous damping, resulting in perfect absorption by critical coupling. Besides, it is shown that the resistance of the resonator, hence the intrinsic damping, can be controlled by the wave amplitude, which provides a way for perfect absorption tuned by nonlinear mechanisms. The perfect absorber that we propose, without moving parts or added material, is simple, robust and it presents a deeply subwavelength ratio wavelength/size $\simeq 18$.
1810.09884v1
2018-12-16
Damping of sound waves by bulk viscosity in reacting gases
The very long standing problem of sound waves propagation in fluids is reexamined. In particular, from the analysis of the wave damping in reacting gases following the work of Einsten \citep{Ein}, it is found that the damping due to the chemical reactions occurs nonetheless the second (bulk) viscosity introduced by Landau \& Lifshitz \citep{LL86} is zero. The simple but important case of a recombining Hydrogen plasma is examined.
1812.06478v1
2019-02-27
Forward Discretely Self-Similar Solutions of the MHD Equations and the Viscoelastic Navier-Stokes Equations with Damping
In this paper, we prove the existence of forward discretely self-similar solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping with large weak $L^3$ initial data. The same proving techniques are also applied to construct self-similar solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping with large weak $L^3$ initial data. This approach is based on [Z. Bradshaw and T.-P. Tsai, Ann. Henri Poincar'{e}, vol. 18, no. 3, 1095-1119, 2017].
1902.10771v3
2019-03-11
The effect of magnetic twist on resonant absorption of slow sausage waves in magnetic flux tubes
Observations show that twisted magnetic flux tubes are present throughout the sun's atmosphere. The main aim of this work is to obtain the damping rate of sausage modes in the presence of magnetic twist. Using the connection formulae obtained by Sakurai et al. (1991), we investigate resonant absorption of the sausage modes in the slow continuum under photosphere conditions. We derive the dispersion relation and solve it numerically and consequently obtain the frequencies and damping rates of the slow surface sausage modes. We conclude that the magnetic twist can result in strong damping in comparison with the untwisted case.
1903.04171v1
2019-03-14
Endpoint Strichartz estimate for the damped wave equation and its application
Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz estimate in the wave endpoint case. We slightly modify the argument of Keel--Tao. Moreover, we apply the endpoint Strichartz estimate to the unconditional uniqueness for the energy critical nonlinear damped wave equation. This problem seems not to be solvable as the perturbation of the wave equation.
1903.05891v2
2019-04-02
Linear inviscid damping in Gevrey spaces
We prove linear inviscid damping near a general class of monotone shear flows in a finite channel, in Gevrey spaces. It is an essential step towards proving nonlinear inviscid damping for general shear flows that are not close to the Couette flow, which is a major open problem in 2d Euler equations.
1904.01188v2
2019-04-16
Damping modes of harmonic oscillator in open quantum systems
Through a set of generators that preserves the hermiticity and trace of density matrices, we analyze the damping of harmonic oscillator in open quantum systems into four modes, distinguished by their specific effects on the covariance matrix of position and momentum of the oscillator. The damping modes could either cause exponential decay to the initial covariance matrix or shift its components. They have to act together properly in actual dynamics to ensure that the generalized uncertainty relation is satisfied. We use a few quantum master equations to illustrate the results.
1904.07452v2
2019-05-20
Stabilization of two strongly coupled hyperbolic equations in exterior domains
In this paper we study the behavior of the total energy and the $L^2$-norm of solutions of two coupled hyperbolic equations by velocities in exterior domains. Only one of the two equations is directly damped by a localized damping term. We show that, when the damping set contains the coupling one and the coupling term is effective at infinity and on captive region, then the total energy decays uniformly and the $L^2$-norm of smooth solutions is bounded. In the case of two Klein-Gordon equations with equal speeds we deduce an exponential decay of the energy.
1905.08370v1
2019-06-02
Mixed control of vibrational systems
We consider new performance measures for vibrational systems based on the $H_2$ norm of linear time invariant systems. New measures will be used as an optimization criterion for the optimal damping of vibrational systems. We consider both theoretical and concrete cases in order to show how new measures stack up against the standard measures. The quality and advantages of new measures as well as the behaviour of optimal damping positions and corresponding damping viscosities are illustrated in numerical experiments.
1906.00503v1
2019-06-27
Comments on the linear modified Poisson-Boltzmann equation in electrolyte solution theory
Three analytic results are proposed for a linear form of the modified Poisson-Boltzmann equation in the theory of bulk electrolytes. Comparison is also made with the mean spherical approximation results. The linear theories predict a transition of the mean electrostatic potential from a Debye-H\"{u}ckel type damped exponential to a damped oscillatory behaviour as the electrolyte concentration increases beyond a critical value. The screening length decreases with increasing concentration when the mean electrostatic potential is damped oscillatory. A comparison is made with one set of recent experimental screening results for aqueous NaCl electrolytes.
1906.11584v1
2019-09-19
Growth rate and gain of stimulated Brillouin scattering considering nonlinear Landau damping due to particle trapping
Growth rate and gain of SBS considering the reduced Landau damping due to particle trapping has been proposed to predict the growth and average level of SBS reflectivity. Due to particle trapping, the reduced Landau damping has been taken used of to calculate the gain of SBS, which will make the simulation data of SBS average reflectivity be consistent to the Tang model better. This work will solve the pending questions in laser-plasma interaction and have wide applications in parametric instabilities.
1909.11606v1
2019-11-26
Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping
The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term $\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded domain $\Omega\subset\mathbb{R}^N$ with Dirichlet boundary conditions. Under some restrictions on $\beta(t)$ and critical growth restrictions on the nonlinear term $f$, we will prove the local and global well-posedness of the solution and derive the existence of a pullback attractor for the process associated with the degenerate damped hyperbolic problem.
1911.11432v1
2019-12-18
Blow-up criteria for linearly damped nonlinear Schrödinger equations
We consider the Cauchy problem for linearly damped nonlinear Schr\"odinger equations \[ i\partial_t u + \Delta u + i a u= \pm |u|^\alpha u, \quad (t,x) \in [0,\infty) \times \mathbb{R}^N, \] where $a>0$ and $\alpha>0$. We prove the global existence and scattering for a sufficiently large damping parameter in the energy-critical case. We also prove the existence of finite time blow-up $H^1$ solutions to the focusing problem in the mass-critical and mass-supercritical cases.
1912.08752v2
2020-01-17
Bounding the Classical Capacity of Multilevel Damping Quantum Channels
A recent method to certify the classical capacity of quantum communication channels is applied for general damping channels in finite dimension. The method compares the mutual information obtained by coding on the computational and a Fourier basis, which can be obtained by just two local measurement settings and classical optimization. The results for large representative classes of different damping structures are presented.
2001.06486v2
2020-01-27
Robustness of polynomial stability of damped wave equations
In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster's equation, and a wave equation with an acoustic boundary condition. In the case of Webster's equation, we use our results to compute explicit numerical bounds that guarantee the polynomial stability of the perturbed equation.
2001.10033v3
2020-02-09
Fujita modified exponent for scale invariant damped semilinear wave equations
The aim of this paper is to prove a blow up result of the solution for a semilinear scale invariant damped wave equation under a suitable decay condition on radial initial data. The admissible range for the power of the nonlinear term depends both on the damping coefficient and on the pointwise decay order of the initial data. In addition we give an upper bound estimate for the lifespan of the solution, in terms of the power of the nonlinearity, size and growth of initial data.
2002.03418v2
2020-02-16
Blow up results for semi-linear structural damped wave model with nonlinear memory
This article is to study the nonexistence of global solutions to semi-linear structurally damped wave equation with nonlinear memory in $\R^n$ for any space dimensions $n\ge 1$ and for the initial arbitrarily small data being subject to the positivity assumption. We intend to apply the method of a modified test function to establish blow-up results and to overcome some difficulties as well caused by the well-known fractional Laplacian $(-\Delta)^{\sigma/2}$ in structural damping terms.
2002.06582v1
2020-03-04
Existence and uniqueness of solutions to the damped Navier-Stokes equations with Navier boundary conditions for three dimensional incompressible fluid
In this article, we study the solutions of the damped Navier--Stokes equation with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$ with smooth boundary. The existence of the solutions is global with the damped term $\vartheta |u|^{\beta-1}u, \vartheta >0.$ The regularity and uniqueness of solutions with Navier boundary condition is also studied. This extends the existing results in literature.
2003.01903v1
2020-04-22
Logarithmic stabilization of an acoustic system with a damping term of Brinkman type
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Without imposing any hypotheses on the structural properties of the damping term, we identify logarithmic decay of solutions with growing time. Logarithmic decay rate is shown by using a frequency domain method and combines a contradiction argument with the multiplier technique and a new Carleman estimate to carry out a special analysis for the resolvent.
2004.10669v1
2020-05-24
A transmission problem for the Timoshenko system with one local Kelvin-Voigt damping and non-smooth coefficient at the interface
In this paper, we study the indirect stability of Timoshenko system with local or global Kelvin-Voigt damping, under fully Dirichlet or mixed boundary conditions. Unlike the results of H. L. Zhao, K. S. Liu, and C. G. Zhang and of X. Tian and Q. Zhang, in this paper, we consider the Timoshenko system with only one locally or globally distributed Kelvin-Voigt damping. Indeed, we prove that the energy of the system decays polynomially and that the obtained decay rate is in some sense optimal. The method is based on the frequency domain approach combining with multiplier method.
2005.12756v1
2020-06-09
Lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity
This paper is devoted to the lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity $$u_{tt}+\Delta^2u-\Delta u-\omega\Delta u_t+\alpha(t)u_t=|u|^{p-2}u\ln|u|.$$ Finite time blow-up criteria for solutions at both lower and high initial energy levels are established, and an upper bound for the blow-up time is given for each case. Moreover, by constructing a new auxiliary functional and making full use of the strong damping term, a lower bound for the blow-up time is also derived.
2006.05006v1