A Dynamic Problem of Thermoelasticity

A space periodic problem of nonlinear thermoelasticity is considered. For an elastic, linear, isotropic, homogeneous, nonviscous body in small geometry, we obtain a nonlinear system of equations. For small coefficient of the heat extension a we find a time global weak solution of the initial-value problem. The smallness of a is independent of the length of the time interval and of the datas. The space periodicity of the solution is related to the absence of reflected waves. A mixed problem for a bounded domain, even with a smooth boundary, seems to be an open problem. Our work is closely related to that by J. Necas L5J and by J. Necas, A. Novotn and V. Sverak L6J.