Related papers: Dispersion estimates for 1D discrete equations

We consider the wave equation with Dirichlet boundary conditions in the exterior of a cylinder in R 3 and we construct a global in time parametrix to derive sharp dispersion estimates for all frequencies (low and high) and, as a corollary,…

The discrete Schr\"odinger equation on a two-dimensional honeycomb lattice is a fundamental tight-binding approximation model that describes the propagation of waves on graphene. For free evolution, we first show that the degenerate…

This work is devoted to study the relation between regularity and decay of solutions of some dissipative perturbations of the Korteweg-de Vries equation in weighted and asymmetrically weighted Sobolev spaces.

Dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients are considered. The global time decay estimates of $L^p-L^q$ norms of propagators are obtained, and…

We obtain large time decay estimates on weighted $L^p$ spaces for solutions to the wave equation with real-valued potential $V(x)=O(|x|^{-2-a})$, $a>0$, for $|x|>1$.

We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such…

We study dispersive properties of the one-dimensional Schr{\"o}dinger equation with a short-range array of delta interactions. More precisely, we consider the self-adjoint operator obtained by perturbing the free Laplacian on the line with…

We prove optimal (that is, without loss of derivatives) dispersive estimates for the Schrodinger group $e^{it(-\Delta+V)}$ for a class of real-valued potentials $V\in C^k(R^n)$ with $k>(n-3)/2$, where $n=4,5$.

In this paper, we first obtain the temporal decay estimates for weak solutions to the three dimensional generalized Navier-Stokes equations. Then, with these estimates at disposal, we obtain the temporal decay estimates for higher order…

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type estimates.

We prove Strichartz-type estimates for Schroedinger's equation with time-dependent potentials. The time derivative of the potentials need not be integrable, so the total variation of the potentials may be infinite.

In this paper, we prove the restriction estimates for 2D surfaces S:= {(xi1, xi2, xi1^3 +/- xi2^3) : (xi1, xi2) in [0,1]^2} by reducing to Wang-Wu's result on the perturbed paraboloid and to the results on the perturbed hyperboloid obtained…

A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…

In this paper, we investigate the decay property of scattering solutions to the initial value problem for the free Schr\"{o}dinger equation in $\mathbb{R}$. It becomes clear that the rate of time decay is essentially determined by the…

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…

We present abstract inhomogeneous Strichartz estimates for dispersive operators, extending previous work by M. Keel and T. Tao on the one hand, and generalising results of D. Foschi, M. Vilela, M. Nakamura and T. Ozawa on the other hand. It…

The discrete wave equation in a multidimensional uniform space with local defects and sources is considered. The characterization of all possible defect configurations corresponding to given amplitudes of waves at the receivers (detectors)…

A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…

In this article, we study the decay of the solutions of Schr\"odinger equations in the exterior of an obstacle. The main situations we are interested in are the general case (no non-trapping assumptions) or some weakly trapping situations

We study solitary wave solutions of the higher order nonlinear Schrodinger equation for the propagation of short light pulses in an optical fiber. Using a scaling transformation we reduce the equation to a two-parameter canonical form.…