Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions
The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality (DEHVI) which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space. First, by applying surjectivity result for...
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| Veröffentlicht in: | Acta mathematica Sinica. English series Jg. 40; H. 4; S. 1143 - 1160 |
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| Sprache: | Englisch |
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01.04.2024
Springer Nature B.V |
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| ISSN: | 1439-8516, 1439-7617 |
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| Abstract | The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality (DEHVI) which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space. First, by applying surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke’s subgradient, we show the nonempty of the solution set for the parabolic hemivariational inequality. Then, some topological properties of the solution set are established such as boundedness, closedness and convexity. Furthermore, we explore the upper semicontinuity of the solution mapping. Finally, we prove the solution set of the system (DEHVI) is nonempty and the set of all trajectories of (DEHVI) is weakly compact in
C
(
I, X
). |
|---|---|
| AbstractList | The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality (DEHVI) which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space. First, by applying surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke’s subgradient, we show the nonempty of the solution set for the parabolic hemivariational inequality. Then, some topological properties of the solution set are established such as boundedness, closedness and convexity. Furthermore, we explore the upper semicontinuity of the solution mapping. Finally, we prove the solution set of the system (DEHVI) is nonempty and the set of all trajectories of (DEHVI) is weakly compact in C(I, X). The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality (DEHVI) which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space. First, by applying surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke’s subgradient, we show the nonempty of the solution set for the parabolic hemivariational inequality. Then, some topological properties of the solution set are established such as boundedness, closedness and convexity. Furthermore, we explore the upper semicontinuity of the solution mapping. Finally, we prove the solution set of the system (DEHVI) is nonempty and the set of all trajectories of (DEHVI) is weakly compact in C ( I, X ). |
| Author | Liu, Zhen Hai Gan, Chun Mei Zhao, Jing |
| Author_xml | – sequence: 1 givenname: Jing surname: Zhao fullname: Zhao, Jing organization: School of Mathematics and Quantitative Economics, Guangxi University of Finance and Economics – sequence: 2 givenname: Chun Mei surname: Gan fullname: Gan, Chun Mei organization: Guangxi Colleges and Universities Key Laboratory of Optimization Control and Engineering Calculation, Guangxi Minzu University – sequence: 3 givenname: Zhen Hai surname: Liu fullname: Liu, Zhen Hai email: zhhliu@hotmail.com organization: Guangxi Colleges and Universities Key Laboratory of Optimization Control and Engineering Calculation, Guangxi Minzu University |
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| Cites_doi | 10.1137/20M1351436 10.1016/j.na.2010.01.025 10.1007/s10107-010-0433-z 10.1016/j.nonrwa.2020.103246 10.1007/s10107-006-0052-x 10.1016/j.jde.2016.01.012 10.1016/j.nonrwa.2018.02.008 10.1515/anona-2016-0102 10.1007/s10107-008-0230-0 10.1137/120875223 10.1007/s10107-013-0669-5 10.1007/BF02857308 10.1007/s10107-007-0117-5 10.1016/j.jde.2007.09.001 10.1016/S0377-0427(00)00543-4 10.1016/j.jde.2017.05.010 10.1016/j.jfa.2009.11.018 10.1016/S0362-546X(98)00016-9 10.1007/s10898-018-0667-5 10.1007/978-1-4419-9158-4 10.1016/0022-1236(72)90070-5 10.1515/9783110870893 10.1016/j.na.2015.03.019 10.1137/20M1330221 |
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| Keywords | Differential parabolic hemivariational inequality Clarke subdifferential 58C06 parabolic-parabolic system 49J52 hyperbolic-parabolic system 47H05 93C20 existence result 47H04 |
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| SubjectTerms | Banach spaces Clarke's solution Convexity Dynamical systems Evolutionary computation Inequality Mathematics Mathematics and Statistics Nonlinear differential equations Nonlinear equations Ordinary differential equations Parabolic differential equations Topology |
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| Title | Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions |
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