Large Solutions and Smoothing Properties for Nonlinear Thermoelastic Systems

We study the existence of global solutions for large data for a class of systems of thermoelastic type with non-local nonlinearities. Moreover, we investigate smoothing properties of such coupled systems in an abstract setting, including some models for thermoelastic plates. In this setting, classical second-order thermoelasticity and viscoleasticity of integral type are recognized as limiting cases. Decay rates of Sobolev norms of the solutions as time tends to infinity are also investigated.