An inverse problem for a double phase implicit obstacle problem with multivalued terms
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Date
2023-04-27
Authors
Zeng, Shengda
Bai, Yunru
Radulescu, Vicentiu
Winkert, Patrick
ORCID
0000-0003-4615-5537Advisor
Referee
Mark
Journal Title
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Volume Title
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Altmetrics
Abstract
In this paper, we study an inverse problem of estimating three discontinuous parameters in a double phase implicit obstacle problem with multivalued terms and mixed boundary conditions which is formulated by a regularized optimal control problem. Under very general assumptions, we introduce a multivalued function called a parameter-to-solution map which admits weakly compact values. Then, by employing the Aubin-Cellina convergence theorem and the theory of nonsmooth analysis, we prove that the parameter-to-solution map is bounded and continuous in the sense of Kuratowski. Finally, a generalized regularization framework for the inverse problem is developed and a new existence theorem is provided.
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Citation
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. 2023, vol. 29, issue 30, p. 1-30.
https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:000977790200001
https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:000977790200001
Document type
Peer-reviewed
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Published version
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en