A Differential Equation Approach to Evolutionary Quasi-Variational Inequalities Arising in Contact Problems

Abstract

In this paper, we consider a class of evolutionary quasi-variational inequalities arising in the study of contact problems for viscoelastic materials. Based on convex analysis methods and fixed point arguments, we prove the well-posedness and regularity of solutions in a general framework. Then, we establish the correspondence between evolutionary variational inequalities and implicit sweeping processes, which enables us to prove an existence result for history-dependent implicit sweeping processes. Finally, our theoretical results are illustrated with an application to contact mechanics problems for viscoelastic materials with a short memory.