{"title":"Evolutionary Quasi-variational Hemivariational Inequalities: Existence and Parameter Identification","authors":"Zijia Peng, Guangkun Yang, Zhenhai Liu, Stanislaw Migórski","doi":"10.1007/s00245-023-10100-7","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with an evolutionary quasi-variational hemivariational inequality in which both the convex and nonconvex energy functionals depend on the unknown solution. The inequality serves as a direct problem of the inverse problem of parameters identification. Employing a fixed point argument and tools from nonlinear analysis, we establish the solvability and weak compactness of the solution set to the direct problem. Then, general existence and weak compactness results for the regularized optimization inverse problem have been proved. Moreover, we illustrate the applicability of the results by an identification problem for an initial-boundary value problem of parabolic type with mixed multivalued and nonmonotone boundary conditions and a state constraint.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 2","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-023-10100-7","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with an evolutionary quasi-variational hemivariational inequality in which both the convex and nonconvex energy functionals depend on the unknown solution. The inequality serves as a direct problem of the inverse problem of parameters identification. Employing a fixed point argument and tools from nonlinear analysis, we establish the solvability and weak compactness of the solution set to the direct problem. Then, general existence and weak compactness results for the regularized optimization inverse problem have been proved. Moreover, we illustrate the applicability of the results by an identification problem for an initial-boundary value problem of parabolic type with mixed multivalued and nonmonotone boundary conditions and a state constraint.
期刊介绍：
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.
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