On an Electro-Magneto-Elasto-Dynamic Transmission Problem

TL;DR

This paper studies a coupled acoustic-elastic system with interface interactions, proving well-posedness and causal dependence in a Hilbert space framework without regularity constraints.

Contribution

It introduces a novel analysis of an electro-magneto-elasto-dynamic transmission problem with minimal regularity assumptions.

Findings

Proves evolutionary well-posedness of the coupled system.

Establishes causal dependence of solutions.

Works in a general Hilbert space setting without boundary regularity constraints.

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.