Related papers: The wave equation on Damek-Ricci spaces
We study linear dispersive equations in dimension one and two for a class of radial nonhomogeneous phases. L 1 $\rightarrow$ L $\infty$ type estimates, Strichartz estimates, local Kato smoothing and Morawetz type estimates are provided. We…
We consider the nonlinear Schrodinger equation under a partial quadratic confinement. We show that the global dispersion corresponding to the direction(s) with no potential is enough to prove global in time Strichartz estimates, from which…
In this paper we study Strichartz estimates for the half wave, the half Klein-Gordon and the Dirac Equations on compact manifolds without boundary, proving in particular for each of these flows local in time estimates both for the wave and…
We obtain Strichartz inequalities for the wave equation with potentials which behave like the inverse square potential $|x|^{-2}$ but might be not a radially symmetric function.
In this paper we obtain some new Strichartz estimates for the wave propagator $e^{it\sqrt{-\Delta}}$ in the context of Wiener amalgam spaces. While it is well understood for the Schr\"odinger case, nothing is known about the wave…
We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non trivial topology: the Poincar\'e dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to…
Wave propagation is studied in a sufficiently anisotropic random medium that backscattering along one direction can be neglected. A Fokker-Planck equation is derived the solution to which would provide a complete statistical description of…
The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of…
Ideas and results of the generalized wave operator theory for dynamical and stationary cases are developed further and exact expressions for generalized scattering operators are obtained for wide classes of differential equations. New…
We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we give an explicit formula for the solution. Also the Limiting…
For the linear damped wave equation (DW), the $L^p$-$L^q$ type estimates have been well studied. Recently, Watanabe showed the Strichartz estimates for DW when $d=2,3$. In the present paper, we give Strichartz estimates for DW in higher…
We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls-Nabarro force the dislocations…
In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
This paper is concerned with the semilinear damped wave equation on a measure space with a self-adjoint operator, instead of the standard Laplace operator. Under a certain decay estimate on the corresponding heat semigroup, we establish the…
We give a method to calculate spectra of the square of the Rarita-Schwinger operator on compact symmetric spaces. According to Weitzenb\"{o}ck formulas, the operator can be written by the Laplace operator, which is the Casimir operator on…
This paper can be considered as a sequel of [BS14] by Bernicot and Samoyeau, where the authors have proposed a general way of deriving Strichartz estimates for the Schr{\"o}dinger equation from a dispersive property of the wave propagator.…
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…
We continue here with previous investigations on the global behavior of general type non-linear wave equations for a class of small, scale-invariant initial data. The method is based on the use of a new set of Strichartz estimates for the…
In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the…