text large_stringlengths 7 3.02k |
|---|
In this work, we consider the 3D defocusing energy-critical nonlinear Schrödinger equation <br>$i\partial_t u+\Delta u =|u|^4 u,\quad (t,x)\in \mathbb{R}\times \mathbb{R}^3$. <br>Applying the outgoing and incoming decomposition presented in the recent work \cite{BECEANU-DENG-SOFFER-WU-2021}, we prove that any radial f... |
We consider a linearized compressible flow structure interaction (FSI) PDE model with a view of analyzing the stability properties of both the compressible flow and plate solution components. In our earlier work, we gave an answer in the affirmative to question of uniform stability for finite energy solutions of said ... |
We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model converges to the classical Lighthill-Whitham-Richards model for traffic flow when t... |
We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues... |
In this paper, we consider the cubic fourth-order nonlinear Schrödinger equation (4NLS) under the periodic boundary condition. We prove two results. |
In the first part of the paper we briefly decribe the classical problem, raised by Monge in 1781, of optimal transportation of mass. We discuss also Kantorovich's weak solution of the problem, which leads to general existence results, to a dual formulation, and to necessary and sufficient optimality conditions. |
In this paper we consider the notion of commutation for a pair of continuous and convex Hamiltonians, given in terms of commutation of their Lax- Oleinik semigroups. This is equivalent to the solvability of an associated multi- time Hamilton-Jacobi equation. |
We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with $(p, q)$-growth. By showing that locally renormalized solutions are essentially bounded below and using Wolff potential estimates, we extend the results of [T. Kilpeläinen, T. Kuu... |
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in the equations and boundary conditions are continuous up to the boundary.... |
We have shown in a recent collaboration that the Cauchy problem for the multi-dimensional Burgers equation is well-posed when the initial data u(0) is taken in the Lebesgue space L 1 (R n), and more generally in L p (R n). We investigate here the situation where u(0) is a bounded measure instead, focusing on the case ... |
Here we construct infinitely many Hölder continuous global-in-time and stationary solutions to the stochastic Euler and hypodissipative Navier-Stokes equations in the space $C(\mathbb{R};C^{\vartheta})$ for $0<\vartheta<\frac{5}{7}\beta$, with $0<\beta< \frac{1}{24}$ and $0<\beta<\min\left\{\frac{1-2\... |
We prove the ill-posedness for the Leray-Hopf weak solutions of the incompressible and ipodissipative Navier-Stokes equations, when the power of the diffusive term $(-\Delta)^\gamma$ is $\gamma < \frac{1}{3}$. We construct infinitely many solutions, starting from the same initial datum, which belong to $C_{x,t}^{\f... |
This short note establishes instability of standing solitary waves in the Euler-Korteweg system. |
In this paper,we will study the boundedness properties of commutator \[ C_{f}=[ f,\Delta] \] acting from $\overset{. }{H}^{1}(\mathbb{R}^{d}) $ to $\overset{. |
This work considers a compressible, viscous, heat-conducting fluid exhibiting thermal relaxation according to Christov's constitutive heat transfer law (C. I. Christov, Mech. |
We consider the limit of sequences of normalized $(s,2)$-Gagliardo seminorms with an oscillating coefficient as $s\to 1$. In a seminal paper by Bourgain, Brezis and Mironescu (subsequently extended by Ponce) it is proven that if the coefficient is constant then this sequence $\Gamma$-converges to a multiple of the Dir... |
In this article we focus on a semiclassical Schrödinger equation with matrix-valued potential presenting a symmetric conjoint crossing of three eigenvalues. The potential we consider is well-known in the chemical literature as a pseudo <br>Jahn-Teller potential. |
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. |
We develop a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara in 1991. This class contains as a special case the Möbius energy. |
We consider the Toda systems of VHS type with singular sources and provide a criterion for the existence of solutions with prescribed asymptotic behaviour near singularities. We also prove the uniqueness of solution. |
In this paper, we study the solvability of a general class of fully nonlinear curvature equations, which can be viewed as generalizations of the equations for Christoffel-Minkowski problem in convex geometry. We will also study the Dirichlet problem of the corresponding degenerate equations as an extension of the equa... |
We study the system \begin{align*}\label{prob:star} \tag{$\star$} \begin{cases} <br>u_t = D_1 \Delta u - \chi_1 \nabla \cdot (u \nabla v) + u(\lambda_1 - \mu_1 u + a_1 |
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand time-asymptotically the solution formulas is proposed, leading to a first term inheriting... |
In this paper we consider an inverse problem for the time dependent linear Boltzmann equation. It concerns the identification of the coefficients via a finite number of measurements on the boundary. |
We solve the existence problem for the minimal positive solutions $u\in L^{p}(\Omega, dx)$ to the Dirichlet problems for sublinear elliptic equations of the form \[ \begin{cases} Lu=\sigma u^q+\mu\qquad \quad \text{in} \quad \Omega, \\ \liminf\limits_{x \rightarrow y}u(x) = 0 \qquad y \in \partial_{\infty}\Omega, \end{... |
We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize this limit function as the ... |
Diffusive limit of the Vlasov-Poisson-Boltzmann system without angular cutoff in the framework of perturbation around global Maxwellian still remains open. By employing the weighted energy method with a newly introduced weight function $w_l(\alpha,\beta)$ and some novel treatments, we solve this problem for the full r... |
We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $\Omega\subset\mathbb{R}^n$. Specifically, for $n\leq 4$ and under mild technical hypotheses on the coefficients and the nonlinearity, we show that there exist open ... |
In this paper, we study a hyperelastic composite material with a periodic microstructure and a prestrain close to a stress-free joint. We consider two limits associated with linearization and homogenization. |
We prove existence of smooth solutions to linear degenerate parabolic equations on bounded domains assuming a structure condition of Fichera. We use this to give a proof of a smooth short time existence result for the porous medium equation $u_t = \Delta u^m$ for $1<m\le 2$. |
The higher-dimensional $b$-equation is a family of PDEs, introduced by Holm and Staley (2003), that describe the motion of shallow water waves in $n$-dimensions. It expresses the invariance of the Lie-transport of the momentum one-form density associated with the fluid in $b$-dimensions. |
We study a two-fluid description of high and low temperature components of the electron velocity distribution of an idealized tokamak plasma. We refine previous results on the laminar steady-state solution. |
We employ Clarkson's inequality to deduce that each extremal of Morrey's inequality is axially symmetric and is antisymmetric with respect to reflection about a plane orthogonal to its axis of symmetry. We also use symmetrization methods to show that each extremal is monotone in the distance from its axis of s... |
In this paper we give a negative answer to the question posed in [15, Open Question 2.1] about possible gains of integrability of determinants of divergence-free, non-negative definite matrix-fields. We also analyze the case in which the matrix-field is given by the Hessian of a convex function. |
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local diffusive interactions. |
We show that a first order perturbation $A(x)\cdot D+q(x)$ of the polyharmonic operator $(-\Delta)^m$, $m\ge 2$, can be determined uniquely from the set of the Cauchy data for the perturbed polyharmonic operator on a bounded domain in $R^n$, $n\ge 3$. Notice that the corresponding result does not hold in general when ... |
In this paper, we investigate on the direct and inverse scattering problem by an unbounded penetrable rough surface in a lossless medium. The cases that the transmission coefficient $\mu\neq1$ and $\mu=1$, which creates certain difficulties in the direct and inverse problem, respectively, are both considered. |
In this paper we study microlocal regularity of a $\mathcal{C}^2$ solution $u$ of the equation \begin{equation*} u_t = f(x,t,u,u_x), \end{equation*} where $f(x,t,\zeta_0, \zeta)$ is ultradifferentiable in the variables $(x,t)\in \mathbb{R}^{N} \times \mathbb{R}$ and holomorphic in the variables $(\zeta_0,\zeta) \in \ma... |
In this paper, we investigate a generic compressible two-fluid model with common pressure ($P^+=P^-$) in $\mathbb{R}^3$. Under some smallness assumptions, Evje-Wang-Wen [Arch Rational Mech Anal 221:1285--1316, 2016] obtained the global solution and its optimal decay rate for the 3D compressible two-fluid model with un... |
Linear transfers between probability distributions were introduced in [5,6] in order to extend the theory of optimal mass transportation while preserving the important duality established by Kantorovich. It is shown here that $\{0, +\infty\}$-valued linear transfers can be characterized by balayage of measures with re... |
We study existence, uniqueness and asymptotic spatial behavior of time-periodic strong solutions to the Navier-Stokes equations in the exterior of a rigid body, $\mathscr B$, moving by time-periodic motion of given period $T$, when the data are sufficiently regular and small. Our contribution improves all previous one... |
Motivated by the astrophysical problems of star formations from molecular clouds,we make the first step on the possible long time behaviors of certain irregularly-shaped molecular clouds. We emphasis the main difficulty of the blowups of the irregular-shaped fluids with vacuum (molecular clouds) comes from the initial... |
We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. |
In this paper, we consider the well-posedness theory of two-dimensional compressible subsonic jet flows for steady full Euler system with general vorticity. Inspired by the analysis in <a href="https://arxiv.org/abs/2006.05672" data-arxiv-id="2006.05672" class="link-https">arXiv:2006.05672</a>, we show that the stream... |
This paper revisits a homogenization problem studied by L. Tartar related to a tridimensional Stokes equation perturbed by a drift (connected to the Coriolis force). Here, a scalar equation and a two-dimensional Stokes equation with a $L^2$-bounded oscillating drift are considered. |
We consider the global well-posedness and decay rates for solutions of 3D incompressible micropolar equation in the critical Besov space. Spectrum analysis allows us to find not only parabolic behaviors of solutions, but also damping effect of angular velocity in the low frequencies. |
We consider the Cauchy problem for the defocusing cubic nonlinear Schrödinger equation in four space dimensions and establish almost sure local well-posedness and conditional almost sure scattering for random initial data in $H^s_x(\mathbb{R}^4)$ with $\frac{1}{3} < s < 1$. The main ingredient in the proofs is t... |
We consider a transport equation by a gradient vector field with a small viscous perturbation --$\epsilon\Delta_g$. We study uniform observability (resp. controllability) properties in the (singular) vanishing viscosity limit $\epsilon\rightarrow 0^+$, that is, the possibility of having a uniformly bounded observation... |
On a closed Riemannian surface $(M,\bar g)$ with negative Euler characteristic, we study the problem of finding conformal metrics with prescribed volume $A>0$ and the property that their Gauss curvatures $f_\lambda= f + \lambda$ are given as the sum of a prescribed function $f \in C^\infty(M)$ and an additive consta... |
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be measurable and uniformly bounded. |
In this paper, we prove the existence of viscosity solutions to complex Hessian equations on compact Hermitian manifolds, assuming the existence of a strict subsolution in the viscosity sense. The results cover the complex Hessian quotient equations. |
We first prove De Giorgi type level estimates for functions in $W^{1,t}(\Omega)$, $\Omega\subset\mathbb{R}^N$, with $t>N\geq 2$. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi's classes as obtained in [Di Benedetto--T... |
In this article, we study the boundary null-controllability properties of the one-dimensional linearized (around $(Q_0,V_0)$ with constants $Q_0>0, V_0>0$) compressible Navier-Stokes equations in the interval $(0,1)$ when a control function is acting either on the density or velocity component at one end of the i... |
Symmetry properties of solutions to elliptic quasilinear equations have been widely studied in the context of Dirichlet boundary conditions. We show that, in the context of Robin boundary conditions, the symmetry property á la Gidas, Ni and Nirenberg does not hold in dimension $n\geq 2$, even for superharmonic functio... |
A class of chemotaxis-Stokes systems generalizing the prototype \[\left\{ \begin{array}{rcl} n_t + u\cdot\nabla n &=& \nabla \cdot \big(n^{m-1}\nabla n\big) - \nabla \cdot \big(n\nabla c\big), c_t + u\cdot\nabla c &=& \Delta c-nc, u_t +\nabla P &=& \Delta u + n \nabla \phi, \qquad \nabla\cdot u ... |
For a $C^2$ function $u$ and an elliptic operator $L$, we prove a quantitative estimate for the derivative $du$ in terms of local bounds on $u$ and $Lu$. An integral version of this estimate is then used to derive a condition for the zero-mean value property of $\Delta u$. |
In this paper we introduce a system coupling a nonlinear Schrödinger equation with a system of viscoelasticity, modeling the interaction between short and long waves, acting for instance on media like plasmas or polymers. We prove the existence and uniqueness of local (in time) strong solutions and the existence of gl... |
Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study integral functionals depending on $X$. Using the results in \cite{MPSC1}, we study the convergence of minima, minimizers and momenta of those functionals. |
We study initial boundary value problems for linear evolution partial differential equations (PDEs) posed on a time-dependent interval $l_1(t)<x<l_2(t)$, $0<t<T$, where $l_1(t)$ and $l_2(t)$ are given, real, differentiable functions, and $T$ is an arbitrary constant. For such problems, we show how to chara... |
We study the contraction of strictly convex, axially symmetric hypersurfaces by a non-symmetric, non-homogeneous, fully nonlinear function of curvature. Starting from axially symmetric hypersurfaces with even profile curves, we show evolving hypersurfaces converge to a point in a finite time, and under proper rescalin... |
We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform volume growth condition. |
We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. |
This paper concerns a free-boundary fluid-structure interaction problem for plaque growth proposed by Yang et al. [J. Math. Biol., 72(4):973--996, 2016] with additional viscoelastic effects, which was also investigated by the authors [arXiv preprint: <a href="https://arxiv.org/abs/2110.00042" data-arxiv-id="2110.00042... |
This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation $$\partial_tu - \partial_x^5u - 30u^2\partial_xu + 20\partial_xu\partial_x^2u + 10u\partial_x^3u = 0.$$ The main results show that regularity or polynomial decay of the data on the positiv... |
It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space $B^{1/3}_{3,\infty}$. When the singular set of the solution is (or belongs to) a smooth manifold, we derive various $L^p$-space regularity criteria dimensionally equivalent to the criti... |
The subject of this paper is to study the decay of solutions for two systems of laminated Timoshenko beams with interfacial slip in the whole space R subject to a thermal effect of type III acting only on one component. When the thermal effect is acting via the second or third component of the laminated Timoshenko bea... |
The theory of abstract Friedrichs operators was introduced some fifteen years ago with the aim of providing a more comprehensive framework for the study of positive symmetric systems of first-order partial differential equations, nowadays better known as (classical) Friedrichs systems. Since then, the theory has not o... |
Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data. Moreover we study the solvability and uniqueness of the weak solutions of problems as... |
In this paper, we consider forward stochastic nonlinear parabolic equations, with a control localized in the drift term. Under suitable assumptions, we prove the small-time global null-controllability, with a truncated nonlinearity. |
We provide an accurate description of the long time dynamics of the solutions of the generalized Korteweg-De Vries (gKdV) and Benjamin-Ono (gBO) equations on the one dimension torus, without external parameters, and that are issued from almost any (in probability and in density) small and smooth initial data. We stres... |
We deal with the viscous profiles for a class of mixed hyperbolic-parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. |
We give some theoretical as well as computational results on Laplace and Maxwell constants. Besides the classical de Rham complex we investigate the complex of elasticity and the complex related to the biharmonic equation and general relativity as well using the general functional analytical concept of Hilbert complex... |
In this paper we study a finite-depth layer of viscous incompressible fluid in dimension $n \ge 2$, modeled by the Navier-Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving interface. |
We present new gradient estimates and Harnack inequalities for positive solutions to nonlinear slow diffusion equations. The framework is that of a smooth metric measure space $(\mathscr M,g,d\mu)$ with invariant weighted measure $d\mu=e^{-\phi} dv_g$ and diffusion operator $\Delta_\phi=e^\phi {\rm div} (e^{-\phi} \na... |
In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, consider a self-adjoint matrix second order elliptic differential operator $\mathcal{B}_\varepsilon$, $0<\varepsilon \leqslant 1$. The principal part of the operator is given in a factorised form, the operator contains first and zero order terms. |
We perform a complete analysis of the limiting behaviour of a class of quasilinear problems with Dirichlet boundary data g. We show that the Lipschitz constant of g plays a role in controlling the Gamma-convergence of the natural energies. |
We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. Here we are motivated by the bounded domain approach with "do-nothing" boundary conditions. |
We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on Hilbert space. Our main result is well-posedness (existence, uniqueness, and stability) for minimax solutions. |
We consider a diffusion problem on a network on whose nodes we impose Dirichlet and generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the associated initial value problem, and we exploit the theory of sub-Markovian and ultracontractive semigroups in order to obtain upper Gaussian estimates f... |
We study the linear stability of flock and mill ring solutions of two individual based models for biological swarming. The individuals interact via a nonlocal interaction potential that is repulsive in the short range and attractive in the long range. |
In this paper, we study the Dirichlet problem for a class of prescribed curvature equations in Minkowski space. We prove the existence of smooth spacelike hypersurfaces with a class of prescribed curvature and general boundary data based on establishing the \emph{a priori} $C^2$ estimates. |
We prove Gaussian upper and lower bounds for the fundamental solutions of a class of degenerate parabolic equations satisfying a weak Hormander condition. The bound is independent of the smoothness of the coefficients and generalizes classical results for uniformly parabolic equations |
We study high energy resonances for the operator $-\Delta_{V,\partial\Omega}:=-\Delta+\delta_{\partial\Omega}\otimes V $ when $V$ has strong frequency dependence. The operator $-\Delta_{V,\partial\Omega}$ is a Hamiltonian used to model both quantum corrals and leaky quantum graphs. |
We study the solvability of the Zakharov equation $$\Delta^2 u + (\kappa-\omega^2)\Delta u - \kappa \,\text{div} \left(e^{-|\nabla u|^2} \nabla u\right) = 0$$ in a bounded domain under homogeneous Dirichlet or Navier boundary conditions. This problem is a consequence of the system of equations derived by Zakharov to m... |
In this paper we consider a multi-dimensional damped semiliear wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. We firstly prove the local existence by using the Faedo-Galerkin approximations combined with a contraction mapping theorem. |
In composite material, the stress may be arbitrarily large in the narrow region between two close-to-touching hard inclusions. The stress is represented by the gradient of a solution to the Lamé system of linear elasticity. |
In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderón's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. |
We investigate a general question about the size and regularity of the data and the solutions in implicit function problems with loss of regularity. First, we give a heuristic explanation of the fact that the optimal data size found by Ekeland and Séré with their recent non-quadratic version of the Nash-Moser theorem ... |
We consider critical points of the energy $E(v) := \int_{\mathbb{R}^n} |\nabla^s v|^{\frac{n}{s}}$, where $v$ maps locally into the sphere or $SO(N)$, and $\nabla^s = (\partial_1^s,\ldots,\partial_n^s)$ is the formal fractional gradient, i.e. $\partial_\alpha^s$ is a composition of the fractional laplacian with the $\a... |
These lecture notes present the quantitative harmonic approximation result for quadratic optimal transport and general measures obtained by Goldman and Otto. The aim is to give a clear presentation of the proof of the main theorem with more motivations, less PDE machinery, and a number of simplifications. |
We perform a systematic study of optimization problems in the Wasserstein spaces that are analogs of infinite horizon, deterministic control problems. We derive necessary conditions on action minimizing paths and present a sufficient condition for their existence. |
In 1993, Chemin proved that vorticity possessing negative Holder regularity in directions given by a sufficient family of vector fields (striated regularity) maintains such regularity for all time when measured against the push-forward of those vector fields. Later work of Gamblin and Saint Raymond, and of Danchin, es... |
In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction $-u^p$, $p>1$ and set in $\R^N$. We consider a bounded, nonnegative initial datum $u_0$ that behaves like a negative power at infinity. |
This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H. Al-Jaboori and D. Wirosoetisno (2011) had proved that the global attractor collapses to ... |
In this paper, we study the following coupled Choquard system in $\mathbb R^N$: $$\left\{\begin{align}&-\Delta u+A(x)u=\frac{2p}{p+q} \bigl(I_\alpha\ast |v|^q\bigr)|u|^{p-2}u,\\ &-\Delta v+B(x)v=\frac{2q}{p+q}\bigl(I_\alpha\ast|u|^p\bigr)|v|^{q-2}v,\\ &\ u(x)\to0\ \ \hbox{and}\ \ v(x)\to0\ \ \hbox{as}\ |x|\... |
We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel $\mathbb{T} \times \mathbb{R}$. Under a simple spectral stability assumption on a self-adjoint operator, we prove a local form of the linear ... |
We introduce a long wave scaling for the Vlasov-Poisson equation and derive, in the cold ions limit, the Korteweg-De Vries equation (in 1D) and the Zakharov-Kuznetsov equation (in higher dimensions, in the presence of an external magnetic field). The proofs are based on the relative entropy method. |
We consider the nonlinear Schr{ö}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and the nonlinearity are asymptotically negligible for large time. |
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. |
We prove the existence of a ground state of the Maxwell--Schrödinger equations in one spatial dimension, describing a specified amount of free charge under the influence of a fixed charge. For one case (equal free and fixed charge, i.e., a neutral atom), we introduce a new type of quartic Banach space, in which the Ha... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.