The Cauchy problem for a nonlinear magnetoelastic system in 1-D periodically inhomogeneous media

We prove the existence and uniqueness of a solution to the Cauchy problem on torus for a magnetoelastic system. The mathematical model consists of three coupled partial differential equations. One of them is a hyperbolic equation describing the elastic medium and the other two equations form a parabolic system originated from the diffusion Maxwell equations. Experimental measurements suggest that the electrically conducting elastic medium has a periodic structure with a finite number of discontinuities in the fundamental domain.