Smoothing Properties, Decay, and Global Existence of Solutions to Nonlinear Coupled Systems of Thermoelastic Type

We consider a nonlinear coupled system of evolution equations, the simplest of which models a thermoelastic plate. Smoothing and decay properties of solutions are investigated as well as the local well-posedness and the global existence of solutions. For the system of standard thermoelasticity it is proved that there is no similar smoothing effect.