A dynamic problem of thermoelasticity (Q1188366)

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 data. 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.