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

The aim of this paper is to examine an inverse problem of parameter identification in an evolutionary quasi-variational hemivariational inequality in infinite dimensional reflexive 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 non-linear 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 non-monotone boundary conditions and a state constraint.