VARIATIONAL ANALYSIS OF A VISCOELASTIC FRICTIONAL CONTACT WITH LONG-TERM MEMORY BODY WITH THERMAL EFFECTS

In this article we study a mathematical model which describes the quasi-static process of contact between a piezoelectric body with long-term memory and an obstacle. The contact is modeled with a normal conformity condition and a version of Coulom's law. The evolution of temperature is described by a first kind evolution equation. The problem is formulated as a system of scalable elliptical variational inequalities for displacement, and a variational equality for electrical stress. We prove the existence of a unique weak solution to the problem. The proof is based on arguments from time-dependent variational inequalities, differential equations and fixed point.