Smoothing Effect and Propagations of Singularities for Viscoelastic Plates

We study dissipative models for plates and we show that the solutions have a smoothing effect on the initial data for viscous plates, while for materials with memory the solution propagates singularities, that is, the solution of the plate equation of memory type is as regular as the initial data. Moreover, we show that when both dissipations are present, the memory type prevails in the sense that the solution propagates singularities. Finally, we prove the existence of global solutions for non-linear dissipative equations, with small data, which decay exponentially as time goes to infinity