Inverse problems for evolutionary quasi-variational hemivariational inequalities with application to mixed boundary value problems

Abstract

The aim of this paper is to examine an inverse problem of parameter identification in an evolutionary quasi-variational hemivariational inequality in in nite dimensional re exive Banach spaces. First, the solvability and compactness of the solution set to the inequality are established by employing a fixed point argument and tools of nonlinear analysis. Then, general existence and compactness results for the inverse problem have been proved. Finally, we illustrate the applicability of the results in the study of an identification problem for an initial-boundary value problem of parabolic type with mixed multivalued and nonmonotone boundary conditions and a state constraint.