| As a kind of important generalization of variational inequality,hemivariational inequality has become an important part of nonlinear analysis and non-smooth analysis,which has been widely applied in mechanics,engineering and other practical problems.Due to the involved time variable,evolutionary hemivariational inequality is dynamic and thus more complicated.Also,evolutionary hemivariational inequality has important applications and research value in practical problems such as mechanics.Among the research on hemivariational inequalities,it is very important to study the solvability of different hemivariational inequality problems and their applications in practical problems.However,in reality,the hemivariational inequalities based on practical problems are always perturbed since the accurate data is almost impossible to obtain.The obtained hemivariational inequalities are always ill-posed,which means that the problems may have either no solution or multiple solutions.Therefore,it is very significant to study stability analysis of the hemivariational inequality.In the present paper,we consider a class of evolutionary second order variational-hemivariational inequality with constrained set.We use surjective theorem and fixed point theorem for history-dependent operator to study unique solvability of the considered problem and introduce the Browder-Tikhonov regularization method to investigate stability analysis of solution to the evolutionary second order variational-hemivariational inequality with constrained set.The details are as follows:In chapter 3,we present the assumptions on the data of the evolutionary second order variational-hemivariational inequality with constrained set and prove its unique solvability.We transform the evolutionary second order variational-hemivariational inequality with constrained set into a corresponding first-order problem by using integral operator,which permits us to use surjective theorem and fixed point theorem for history-dependent operators to prove the unique solvability of the evolutionary second order variational-hemivariational inequality with constrained set with the help of relative inclusion problem.In chapter 4,we introduce the perturbed problem and the regularized problem,whose data including the constraint set are perturbed,to analyze stability of solutions to the evolutionary second order variational-hemivariational inequality with constrained set.First,we use its perturbed data and the duality mapping to construct the perturbed and regu-larized problems for the evolutionary second order variational-hemivariational inequality with constrained set.Then,we state that the perturbed and regularized problems are unique solvable.Finally,we obtain two sequences,called approximating sequences of solution to the evolutionary second order variational-hemivariational inequality with constrained set,and prove that both of the approximating sequences can converge strongly to the solution of the evolutionary second order variational-hemivariational inequality with constrained set under suitable conditions. |
