Well-posedness of the Cauchy problem to a nonlinear magnetoelastic system in 1-D periodic media
Wladimir Neves, Viatcheslav Ivanovich Priimenko, Mikhail P. Vishnevskii · Journal of Inverse and Ill-Posed Problems · 2012
Abstract. There is studied well-posedness of the Cauchy problem on torus to 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 diffusion 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 studied in this paper the problem which we have defined as periodically Cauchy diffraction problem. The basic result is to prove existence, uniqueness and stability of solutions of the formulated problem.