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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 th...
1503.04356v1
2015-04-23
Magnetization damping in noncollinear spin valves with antiferromagnetic interlayer couplings
We study the magnetic damping in the simplest of synthetic antiferromagnets, i.e. antiferromagnetically exchange-coupled spin valves in which applied magnetic fields tune the magnetic configuration to become noncollinear. We formulate the dynamic exchange of spin currents in a noncollinear texture based on the spindiff...
1504.06042v1
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 sourc...
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 re...
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 dif...
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 li...
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 particle...
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 pro...
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 yiel...
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...
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 s...
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 al...
1603.00233v2
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 \ti...
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 ...
1604.07607v1
2016-05-05
Theory of magnon motive force in chiral ferromagnets
We predict that magnon motive force can lead to temperature dependent, nonlinear chiral damping in both conducting and insulating ferromagnets. We estimate that this damping can significantly influence the motion of skyrmions and domain walls at finite temperatures. We also find that in systems with low Gilbert damping...
1605.01694v2
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 \...
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...
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 ...
1609.01436v1
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 emulat...
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 explici...
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 syste...
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....
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...
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 conf...
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 f...
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 cont...
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...
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 dampin...
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 n...
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 $1<p<p_S(n+...
1709.00866v2
2017-09-13
Life-span of blowup solutions to semilinear wave equation with space-dependent critical damping
This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical space-dependent damping term (DW:$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\le...
1709.04401v1
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...
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 effectiv...
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 relate...
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. C...
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 iteratio...
1803.05126v2
2018-04-19
Damping of magnetization dynamics by phonon pumping
We theoretically investigate pumping of phonons by the dynamics of a magnetic film into a non-magnetic contact. The enhanced damping due to the loss of energy and angular momentum shows interference patterns as a function of resonance frequency and magnetic film thickness that cannot be described by viscous ("Gilbert")...
1804.07080v2
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 dime...
1805.11975v1
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-V...
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 base...
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...
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 th...
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...
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, other...
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 ...
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 ...
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...
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 Lan...
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...
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 m...
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 un...
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 cau...
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 ...
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...
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 exp...
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 ...
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 restrictio...
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 ener...
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 classi...
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 e...
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 initi...
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 functio...
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 solut...
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 combi...
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 loca...
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 boun...
2006.05006v1
2020-07-05
Oscillation of damped second order quasilinear wave equations with mixed arguments
Following the previous work [1], we investigate the impact of damping on the oscillation of smooth solutions to some kind of quasilinear wave equations with Robin and Dirichlet boundary condition. By using generalized Riccati transformation and technical inequality method, we give some sufficient conditions to guarante...
2007.02284v1
2020-07-08
A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term
In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in $\mathbb{R}^n$, which can be represented by the Riemann-Liouville fractional integral of order $1-\gamma$ with $\gamma\in(0,1)$. Our main interest is to study mixed influence from da...
2007.03954v2
2020-08-02
Quantum capacity analysis of multi-level amplitude damping channels
The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension $d$. In the special case of $d=3$, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the a...
2008.00477v3
2020-08-11
An inverse spectral problem for a damped wave operator
This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting a sequence of trace formulas, which are deduced by a recursive formula, bridgin...
2008.04523v1
2020-08-17
Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I
In this paper, we are interested in the Cauchy problem for the viscoelastic damped wave equation with memory of type I. By applying WKB analysis and Fourier analysis, we explain the memory's influence on dissipative structures and asymptotic profiles of solutions to the model with weighted $L^1$ initial data. Furthermo...
2008.07151v1
2020-08-18
A class of Finite difference Methods for solving inhomogeneous damped wave equations
In this paper, a class of finite difference numerical techniques is presented to solve the second-order linear inhomogeneous damped wave equation. The consistency, stability, and convergences of these numerical schemes are discussed. The results obtained are compared to the exact solution, ordinary explicit, implicit f...
2008.08043v2
2020-09-10
Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein-de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we conjecture an expression for the critical exponent due to the main blow-up results, which...
2009.05372v1
2020-09-11
Asymptotic profiles for a wave equation with parameter dependent logarithmic damping
We study a nonlocal wave equation with logarithmic damping which is rather weak in the low frequency zone as compared with frequently studied strong damping case. We consider the Cauchy problem for this model in the whole space and we study the asymptotic profile and optimal estimates of the solutions and the total ene...
2009.06395v1
2020-09-17
Sensitivity of steady states in a degenerately-damped stochastic Lorenz system
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant probability measure if and only if noise acts on the convection variable. On the...
2009.08429v1
2021-01-23
Oscillation time and damping coefficients in a nonlinear pendulum
We establish a relationship between the normalized damping coefficients and the time that takes a nonlinear pendulum to complete one oscillation starting from an initial position with vanishing velocity. We establish some conditions on the nonlinear restitution force so that this oscillation time does not depend monoto...
2101.09400v2
2021-02-20
Lifespan estimates for semilinear wave equations with space dependent damping and potential
In this work, we investigate the influence of general damping and potential terms on the blow-up and lifespan estimates for energy solutions to power-type semilinear wave equations. The space-dependent damping and potential functions are assumed to be critical or short range, spherically symmetric perturbation. The blo...
2102.10257v1
2021-02-24
Attractors for locally damped Bresse systems and a unique continuation property
This paper is devoted to Bresse systems, a robust model for circular beams, given by a set of three coupled wave equations. The main objective is to establish the existence of global attractors for dynamics of semilinear problems with localized damping. In order to deal with localized damping a unique continuation prop...
2102.12025v1
2021-03-09
Global weak solution of 3D-NSE with exponential damping
In this paper we prove the global existence of incompressible Navier-Stokes equations with damping $\alpha (e^{\beta |u|^2}-1)u$, where we use Friedrich method and some new tools. The delicate problem in the construction of a global solution, is the passage to the limit in exponential nonlinear term. To solve this prob...
2103.05388v1
2021-05-03
Enhanced and unenhanced dampings of the Kolmogorov flow
In the present study, Kolmogorov flow represents the stationary sinusoidal solution $(\sin y,0)$ to a two-dimensional spatially periodic Navier-Stokes system, driven by an external force. This system admits the additional non-stationary solution $(\sin y,0)+e^{-\nu t} (\sin y,0)$, which tends exponentially to the Kolmo...
2105.00730v3
2021-05-06
On Linear Damping Around Inhomogeneous Stationary States of the Vlasov-HMF Model
We study the dynamics of perturbations around an inhomogeneous stationary state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized stability criterion (Penrose criterion). We consider solutions of the linearized equation around the steady state, and prove the algebraic decay in time of the Fourie...
2105.02484v1
2021-05-31
Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition
It has been established that solutions to the inviscid Proudman-Johnson equation subject to a homogeneous three-point boundary condition can develop singularities in finite time. In this paper, we consider the possibility of singularity formation in solutions of the generalized, inviscid Proudman-Johnson equation with ...
2106.00068v1
2021-06-16
Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations
The dependence of the fractal dimension of global attractors for the damped 3D Euler--Bardina equations on the regularization parameter $\alpha>0$ and Ekman damping coefficient $\gamma>0$ is studied. We present explicit upper bounds for this dimension for the case of the whole space, periodic boundary conditions, and t...
2106.09077v1
2021-06-23
Damping of the Franz-Keldysh oscillations in the presence of disorder
Franz-Keldysh oscillations of the optical absorption in the presence of short-range disorder are studied theoretically. The magnitude of the effect depends on the relation between the mean-free path in a zero field and the distance between the turning points in electric field. Damping of the Franz-Keldysh oscillations ...
2106.12691v1
2021-06-25
Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems
In Hilbert space, we propose a family of primal-dual dynamical system for affine constrained convex optimization problem. Several damping coefficients, time scaling coefficients, and perturbation terms are thus considered. By constructing the energy functions, we investigate the convergence rates with different choices...
2106.13702v1
2021-07-01
Event-triggering mechanism to damp the linear wave equation
This paper aims at proposing a sufficient matrix inequality condition to carry out the global exponential stability of the wave equation under an event-triggering mechanism that updates a damping source term. The damping is distributed in the whole space but sampled in time. The wellposedness of the closed-loop event-t...
2107.00292v1
2022-01-28
Quantum metrology with a non-linear kicked Mach-Zehnder interferometer
We study the sensitivity of a Mach-Zehnder interferometer that contains in addition to the phase shifter a non-linear element. By including both elements in a cavity or a loop that the light transverses many times, a non-linear kicked version of the interferometer arises. We study its sensitivity as function of the pha...
2201.12255v1
2022-02-27
The time asymptotic expansion for the compressible Euler equations with time-dependent damping
In this paper, we study the compressible Euler equations with time-dependent damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation (GPME) and rigorously justify this expansion as $\lambda \in (\frac17,1)$. In other wo...
2202.13385v1
2022-03-12
Stability for nonlinear wave motions damped by time-dependent frictions
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any bifurcation and chaos. And it is a sharp condition on the damping coefficient for th...
2203.06312v1
2022-03-30
A Toy Model for Damped Water Waves
We consider a toy model for a damped water waves system in a domain $\Omega_t \subset \mathbb{T} \times \mathbb{R}$. The toy model is based on the paradifferential water waves equation derived in the work of Alazard-Burq-Zuily. The form of damping we utilize we utilize is a modified sponge layer proposed for the three-...
2203.16645v1
2022-05-10
Global attractor for the weakly damped forced Kawahara equation on the torus
We study the long time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in $L^2$, to which as time passes all solutions draw closer. In fact, we show that the global attractor turns out to lie in a smoother space $H^2$ and b...
2205.04642v1
2022-06-07
Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data
We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the power of the nonlinearity, and the decay rate of the initial data at the spatia...
2206.03218v2
2022-10-24
The time asymptotic expansion for the compressible Euler equations with damping
In 1992, Hsiao and Liu \cite{Hsiao-Liu-1} firstly showed that the solution to the compressible Euler equations with damping time-asymptotically converges to the diffusion wave $(\bar v, \bar u)$ of the porous media equation. In \cite{Geng-Huang-Jin-Wu}, we proposed a time-asymptotic expansion around the diffusion wave ...
2210.13157v1
2022-12-18
Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions
We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based on the study of the corresponding hyperbolic systems associated with the Riemann ...
2212.09164v1
2023-02-09
A remark on the logarithmic decay of the damped wave and Schrödinger equations on a compact Riemannian manifold
In this paper we consider a compact Riemannian manifold (M, g) of class C 1 $\cap$ W 2,$\infty$ and the damped wave or Schr\"odinger equations on M , under the action of a damping function a = a(x). We establish the following fact: if the measure of the set {x $\in$ M ; a(x) = 0} is strictly positive, then the decay in...
2302.04498v1
2023-03-02
Using vibrating wire in non-linear regime as a thermometer in superfluid $^3$He-B
Vibrating wires are common temperature probes in $^3$He experiments. By measuring mechanical resonance of a wire driven by AC current in magnetic field one can directly obtain temperature-dependent viscous damping. This is easy to do in a linear regime where wire velocity is small enough and damping force is proportion...
2303.01189v1
2023-04-06
A turbulent study for a damped Navier-Stokes equation: turbulence and problems
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and with a particular choice of the damping parameter, when the Grashof numbers are la...
2304.03134v1
2023-05-03
Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions
We establish the exponential decay of the solutions of the damped wave equations in one-dimensional space where the damping coefficient is a nowhere-vanishing function of space. The considered PDE is associated with several dynamic boundary conditions, also referred to as Wentzell/Ventzel boundary conditions in the lit...
2305.01969v2