We consider the 0-order perturbed Lamé operator− Δ⁎+ V (x). It is well known that if one
considers the free case, namely V= 0, the spectrum of− Δ⁎ is purely continuous and …

In this paper we investigate spectral properties of the damped elastic wave equation.
Deducing a correspondence between the eigenvalue problem of this model and the one of …

This paper is devoted to providing quantitative bounds on the location of eigenvalues, both
discrete and embedded, of non self-adjoint Lamé operators of elasticity− Δ⁎+ V in terms of …

In this paper, we describe a constructive method to find a dissipative term for any generic
higher order, homogeneous, possibly weakly, hyperbolic operator, with x∈ ℝ n, n≥ 1. We …

We obtain weighted $ L^ 2$ estimates for the elastic wave equation perturbed by singular
potentials including the inverse-square potential. We then deduce the Strichartz estimates …

We prove dispersive estimate for the elastic wave equation by which we extend the known
Strichartz estimates for the classical wave equation to those for the elastic wave equation. In …

We study pointwise convergence of the solution to the elastic wave equation to the initial
data which lies in the Sobolev spaces. We prove that the solution converges along every …

Abstract (EN) Elastic waves describe particles vibrating in materials holding the property of
elasticity. Particularly, several kinds of resistance in elasticity lead to the models of elastic …

The bulk of this thesis focuses on two fields that are being deeply investigated both by the
mathematical and physical community, namely spectral theory and unique continuation …

We consider the $0 $-order perturbed Lam\'e operator $-\Delta^\ast+ V (x) $. It is well known
that if one considers the free case, namely $ V= 0, $ the spectrum of $-\Delta^\ast $ is purely …