Convergence of solutions to inverse problems for a class of variational-hemivariational inequalities
Convergence of solutions to inverse problems for a class of variational-hemivariational inequalities
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DOI：
10.3934/dcdsb.2018172
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发表时间：
2018-06
影响因子：
1.2
通讯作者：
S. Migórski;Biao Zeng
中科院分区：
文献类型：
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作者：
S. Migórski;Biao Zeng
研究一类平稳变分-半变分不等式的反问题。变分-半变分不等式的解近似于它的惩罚版本。证明了初始不等式问题和惩罚问题的逆问题解的存在性。我们证明了惩罚问题的反问题的最优解收敛到一个子序列，当惩罚参数趋于零时，收敛到初始变分-半变分不等式的反问题的最优解。用一个非光滑接触问题的弹性数学模型对结果进行了说明。
The paper investigates an inverse problem for a stationary variational-hemivariational inequality. The solution of the variational-hemivariational inequality is approximated by its penalized version. We prove existence of solutions to inverse problems for both the initial inequality problem and the penalized problem. We show that optimal solutions to the inverse problem for the penalized problem converge, up to a subsequence, when the penalty parameter tends to zero, to an optimal solution of the inverse problem for the initial variational-hemivariational inequality. The results are illustrated by a mathematical model of a nonsmooth contact problem from elasticity.