A general differential quasi variational–hemivariational inequality: Well-posedness and application

Abstract

In the paper we analyze a general differential quasi variational-hemivariational inequality in Banach spaces which couples the Cauchy problem for an ordinary differential equation with a quasi variational-hemivariational inequality considered with a unilateral constraint and history-dependent operators. The latter appear in all of the data: the governing nonlinear operator, the generalized directional derivative of a locally Lipschitz potential, a convex potential, and the ordinary differential equation. The results on the well-posedness and regularity of solutions are proved by exploiting a fixed point approach. The theory is illustrated by an application to a quasistatic generalized Signorini unilateral frictional contact problem for viscoplastic materials with a nonsmooth multivalued contact condition.