Asymptotics of the solutions of the stochastic lattice wave equation

In this note we prove that the essential spectrum of a Schrödinger operator with δ-potential supported on a finite number of compact Lipschitz hypersurfaces is given by [0, +∞)..

Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering

We also use this abstract KAM theorem to prove the existence of small amplitude quasi-periodic solutions for the nonlinear wave equation on the circle without parameter (see [4]).

for the heat equation (that is δ = 0 in (2); there, the authors prove a Liouville Theorem which turns to be the trivial case of the Liouville Theorem proved by Merle and Zaag in

Keywords: semilinear elliptic equations; Lin-Ni conjecture; Sobolev inequality; interpo- lation; Gagliardo-Nirenberg inequalities; Keller-Lieb-Thirring inequality; optimal con-

In a third part, the ac- curacy and performance of the resulting homogenization code are challenged on various elastic models: (i) a finely layered medium for which

Keywords and phrases: Stochastic partial differential equations, Malliavin Calculus, wave equation, probability densities.. ∗ Partially supported by the grant ERBF MRX CT960075A of

Since the case of checkerboards (in dimension two) is interesting and challenging, following a question by Nicolas Burq, in the next section we investigate the case of