Inverse problems for constrained parabolic variational-hemivariational inequalities *

Source abstract

Abstract In this paper we study a novel class of inverse problems for parabolic variational–hemivariational inequalities with a unilateral constraint. A theorem on the well-posedness for weak solution is established. Based on a new continuous dependence result, we prove the nonemptiness and stability of the set of optimal solutions to the corresponding inverse problems. We illustrate the results by a quasistatic nonsmooth frictional viscoelastic contact problem with a unilateral constraint for which we derive results on the unique weak solvability, and existence and stability of solutions to the associated inverse problems.