| Abstract: |
| We present recent results on the existence and uniqueness of the solution to the hemivariational inequality of first order with the history-dependent operator. The proof is based on arguments of surjectivity for pseudomonotone operators and the Banach fixed point theorem.
We study also the continuous dependence of the solution to the considered inequality w.r.t. the operators, functions and initial data involved in the problem. The interest in continuous dependence of the solution on the perturbed data is twofold. First, the associated regularized problems can be used in numerical methods. Second, it can be the first step in studying of optimal control and identiffcation problems.
Finally, we consider an example which shows how the abstract result is applicable to the model of the contact problem.
This is a joint contribution with Stanislaw Migorski and Mircea Sofonea. |
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