Related papers: Dispersion estimates for 1D discrete equations

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…

We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…

In this paper we prove dispersive estimates for the system formed by two coupled discrete Schr\"odinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting absorption principle.…

We improve previous results on dispersive decay for 1D Klein- Gordon equation. We develop a novel approach, which allows us to establish the decay in more strong norms and weaken the assumption on the potential.

We derive the long-time decay in weighted norms for solutions of the discrete 3D Schr\"odinger and Klein-Gordon equations.

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Dirac equation. To this end we develop basic scattering theory and establish a limiting absorption principle for discrete perturbed Dirac operators.

We present some old and new results on dispersive estimates for Schroedinger equations.

We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near…

We obtain a dispersive long-time decay in weighted energy norms for solutions of the 1D Dirac equation with generic potential. The decay extends the results obtained by Jensen, Kato and Murata for the Schr\"odinger equations.

We investigate the dispersive properties of solutions to the Schr\"odinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schr\"odinger flow on…

In this paper we analyze the dispersion property of some models involving Schr\"odinger equations. First we focus on the discrete case and then we present some results on graphs.

Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.

We prove the dispersive and Strichartz estimates for solutions to the wave equation with a class of many-electric potentials in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the…

We prove L^1 --> L^\infty estimates for linear Schroedinger equations in dimensions one and three. The potentials are only required to satisfy some mild decay assumptions. No regularity on the potentials is assumed.

We prove some local smoothing estimates for the Schr\"{o}dinger initial value problem with data in $L^2(\mathbb{R}^d)$, $d \geq 2$ and a general class of potentials. In the repulsive setting we have to assume just a power like decay…

We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…

We prove a dispersive estimate for periodic discrete Schr\"odinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates for the discrete nonlinear Schr\"odinger equation with…

In this paper we analyze the dispersion for one dimensional wave and Schrodinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient…

We prove dispersive estimates for linear Schroedinger equations in two space dimensions. The potential is assumed to be real-valued with some polynomial decay (faster than a negative third power), and zero energy is assumed to be a regular…

The purpose of this article is twofold. First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon and Schr{\"o}dinger…