A dynamic electroviscoelastic problem with thermal effects

Abstract

We consider a mathematical model which describes the dynamic
process of contact between a piezoelectric body and an electrically conduc-tive foundation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law with thermal effects. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments.