Well-posedness of the Cauchy Problem on Torus to Electromagnetoelastic System

TL;DR

This paper establishes the well-posedness of the Cauchy problem for a coupled electromagnetoelastic system on a torus, involving hyperbolic and parabolic PDEs, modeling a periodic elastic medium with discontinuities.

Contribution

It proves the well-posedness of a complex coupled PDE system modeling electromagnetoelastic phenomena with periodic and discontinuous structures.

Findings

Proved well-posedness of the coupled PDE system.

Analyzed the periodic structure with discontinuities.

Established mathematical foundation for electromagnetoelastic modeling.

Abstract

We prove the well-posedness of the Cauchy problem on torus to an eletromagnetoelastic system. The physical model consists of three coupled partial differential equations, one of them is a hyperbolic equation describing the elastic medium and two other ones form a parabolic system, which comes from Maxwell's equations. Experimental measurements suggest that the elastic medium has a periodic structure, moreover with finite number of discontinuities on the fundamental domain. Thus we have study in this paper the problem which we have defined as periodically Cauchy diffraction problem.