  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.
