Related papers: Exponential decay for the Schr{\"o}dinger equation…
In this paper we study the well-posedness and stability of degenerate Schr\"{o}dinger equation with a fractional boundary damping. First, we establish the well-posedness of the degenerate problem $\psi_t(x,t)-\imath(\tau(x)…
We improve a previous result about the local energy decay for the damped wave equation on R^d. The problem is governed by a Laplacian associated with a long range perturbation of the flat metric and a short range absorption index. Our…
We study exponential decay of eigenfunctions of self-adjoint higher order elliptic operators on $\R^d$. We show that the possible critical decay rates are determined algebraically. In addition we show absence of super-exponentially decaying…
In this paper we study the behavior of the energy of solutions of the wave equation with localized damping in exterior domain. We assume that the damper is positive at infinity. Under the Geometric Control Condition of Bardos et al (1992),…
We prove that 3-dimensional Schrodinger operator with slowly decaying sparse potential has an a.c. spectrum that fills positive half-line. A new kind of WKB asymptotics for Green's function is found. The absense of positive eigenvalues is…
Two non-equidistant grid implementations of infinite range exterior complex scaling are introduced that allow for perfect absorption in the time dependent Schr\"odinger equation. Finite element discrete variables grid discretizations…
We prove weighted L^2 (Morawetz) estimates for the solutions of linear Schrodinger and wave equation with potentials that decay like |x|^{-2} for large x, by deducing them from estimates on the resolvent of the associated elliptic operator.…
In this paper we study a class of semilinear wave type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able…
We prove dispersive decay, pointwise in time, for solutions to the mass-critical nonlinear Schr\"odinger equation in spatial dimensions $d=1,2,3$.
The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.…
We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation.…
The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced…
Initial-boundary value problems for the linear Zakharov-Kuznetsov equation posed on bounded rectangles are considered. Spectral properties of a stationary operator are studied in order to show that the evolution problem posed on a bounded…
We consider an evolution equation similar to that introduced by Vese and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce,…
In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element…
In this article, we consider the infinite dimensional vector-valued resonant nonlinear Schr\"odinger system, which arises from the study of the asymptotic behavior of the defocusing nonlinear Schr\"{o}dinger equation on "wave guide"…
By refining a recent result of Xie and Zhang, we prove the exponential ergodicity under a weighted variation norm for singular SDEs with drift containing a local integrable term and a coercive term. This result is then extended to singular…
In this paper we analyze a nonlinear abstract evolution equation with an infinite number of time-dependent time delays and a Lipschitz continuous nonlinear term. By using a fixed point argument we prove the existence of a mild solution.…
We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…
We prove Strichartz inequalities for the wave and Schr\"odinger equations on noncompact surfaces with ends of finite area, i.e. with ends isometric to $ \big( (r_0,\infty) \times {\mathbb S}^1 , dr^2 + e^{- 2 \phi (r)}d \theta^2 \big) $…