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

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.