Analyse spectrale d'une bande élastique isotrope stratifiée et applications

Abstract

The operator of linear elasticity A in an isotropic stratified medium ω = {(x 1 , x 2 ) ∈ R 2 ; 0 < x 2 < L} is unitarily equivalent to an operator M, which is a direct sum of a countable family of multiplication operators M n defined in L 2 ( R ). The spectral consequences of obtaining, for the first time, systematic non-monotonicity of the associated dispersion curves, as well as other distinctive features, justify the general framework adopted here, in order to prove a limiting absorption principle which is an important stage in the scattering theory. A whole class of operators can then be immediately treated.