Revisiting the Decoupling of Elastic Waves From a Weak Formulation Perspective

TL;DR

This paper offers a new variational approach to demonstrate the decoupling of elastic waves in scattering problems governed by the Lame system, extending previous boundary behavior analyses.

Contribution

It introduces a novel variational method to establish wave decoupling, providing an alternative proof to prior boundary behavior-based results.

Findings

Decoupling of longitudinal and shear waves under certain boundary conditions.

A variational framework for analyzing elastic wave decoupling.

Extension of previous boundary analysis results.

Abstract

Elastic scattering governed by the Lame system associated with the third-type or fourth-type boundary condition is considered. It was shown in [8] by two of the authors that under suitable geometric conditions on the boundary surface of the elastic inclusion, the longitudinal and shear waves can be decoupled. The decoupling result in [8] was derived based on analyzing the local boundary behaviours of the elastic fields. In this article, we provide a different argument from a variational perspective in proving the decoupling result.