On an Elasto-Acoustic Transmission Problem in Anisotropic, Inhomogeneous Media

TL;DR

This paper analyzes an elasto-acoustic transmission problem in anisotropic, inhomogeneous media, establishing well-posedness of the coupled system with minimal regularity assumptions on the interface.

Contribution

It introduces a novel framework for the coupled elasto-acoustic system with interface conditions, proving well-posedness without regularity constraints.

Findings

Proved evolutionary well-posedness of the coupled system.

Established causal dependence in the solution.

Handled media with anisotropic and inhomogeneous properties.

Abstract

We consider a coupled system describing the interaction between acoustic and elastic regions, where the coupling occurs not via material properties but through an interaction on an interface separating the two regimes. Evolutionary well-posedness in the sense of Hadamard well-posedness supplemented by causal dependence is shown for a natural choice of generalized interface conditions. The results are obtained in a real Hilbert space setting incurring no regularity constraints on the boundary and almost none on the interface of the underlying regions.