A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions

A model for the generation of heat due to mechanical losses during acoustic wave propagation in a solid is considered in a Kelvin–Voigt type framework. In contrast to previous studies on related thermoviscoelastic models, in line with recent experimental findings the present paper focuses on situations in which the elastic parameters depend on the temperature; in particular, this aligns with measurements that reveal an increase of certain components in the elasticity tensor with growing temperature. Despite an apparent loss of mathematically favorable structural properties thereby encountered, in the framework of a suitably generalized concept of solvability a result on global existence of solutions is derived under mild assumptions which, in particular, do not involve any smallness condition on the initial data.