Abstract evolution equations for viscoelastic frictional contact problems

Abstract.

We analyze a nonlinear abstract evolution problem describing a class of frictional contact processes between a viscoelastic body and a foundation. The problem is set as a time-dependent differential inclusion. The existence of a unique solution is established using the theory of elliptic variational inequalities and Banach's fixed point theorem. A dual formulation of the problem is also introduced and an equivalence result between the two problems is proved. Finally, the abstract results obtained are used to solve some frictional contact problems for viscoelastic materials.