Convergence of solutions to inverse problems for a class of variational-hemivariational inequalities

Stanisław Migórski; Biao Zeng

doi:10.3934/dcdsb.2018172

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2018, Volume 23, Issue 10: 4477-4498. Doi: 10.3934/dcdsb.2018172

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Convergence of solutions to inverse problems for a class of variational-hemivariational inequalities

Stanisław Migórski^1,2, and
Biao Zeng^2, ,

1.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610225, Sichuan Province, China
2.
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Chair of Optimization and Control, ul. Lojasiewicza 6, 30-348 Krakow, Poland

* Corresponding author: biao.zeng@outlook.com
* Corresponding author: biao.zeng@outlook.com

Received: April 30, 2017

Revised: December 31, 2017

Early access: May 2018

Published: September 2018

The research is supported by the National Science Center of Poland under Maestro Project No. UMO-2012/06/A/ST1/00262, Special Funds of Guangxi Distinguished Experts Construction Engineering, Guangxi, China, and the International Project cofinanced by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 3792/GGPJ/H2020/2017/0.

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Abstract

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.

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Mathematics Subject Classification: 35R30, 47J20, 49J40, 49N45, 74G75, 74M15, 90C26.

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