This article is cited in 5 papers

Inverse problems for evolutionary quasi-variational hemivariational inequalities with application to mixed boundary value problems

Zijia Peng^ab, Guangkun Yang^ac, Zhenhai Liu^db, S. Migórski<sup>ef

a</sup> College of Mathematics and Physics, Guangxi Minzu University, Nanning, Guangxi, P. R. China
^b Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, Guangxi Minzu University, Nanning, Guangxi, P. R. China
^c Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, Guangxi, P. R. China
^d Center for Applied Mathematics of Guangxi, Yulin Normal University, P. R. China
^e College of Sciences, Beibu Gulf University, Qinzhou, Guangxi, P. R. China
^f Jagiellonian University in Krakow, Krakow, Poland

Abstract: The aim of this paper is to examine an inverse problem of parameter identification in an evolutionary quasi-variational hemivariational inequality in infinite dimensional reflexive Banach spaces. First, the solvability and compactness of the solution set to the inequality are established by employing a fixed point argument and tools of non-linear analysis. Then, general existence and compactness results for the inverse problem have been proved. Finally, we illustrate the applicability of the results in the study of an identification problem for an initial-boundary value problem of parabolic type with mixed multivalued and non-monotone boundary conditions and a state constraint.

Keywords: inverse problem, evolutionary quasi-variational hemivariational inequality, mixed parabolic boundary value problem.

UDC: 517.9

MSC: 35R30, 49J40, 49J53

Received: 14.10.2023
Revised: 17.01.2024

Language: English

DOI: 10.4213/im9551

 English version: Izvestiya: Mathematics, 2024, 88:5, 988–1011

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