Mathematical analysis of the propagation of elastic guided waves in heterogeneous media

AbstractIn this article, we are concerned with the propagation of elastic waves in isotropic heterogeneous media, invariant under translation in one direction. We give a theoretical analysis of the existence of guided waves and of their properties. In particular the thresholds, or cut-off frequencies, are studied in detail. The main mathematical tool is the spectral theory of selfadjoint operators, and more specifically the Max-Min principle

Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms

We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples