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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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 40; no. 4; pp. 1143 - 1160
Main Authors: Zhao, Jing, Gan, Chun Mei, Liu, Zhen Hai
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024
Springer Nature B.V
Subjects:
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
Differential parabolic hemivariational inequality
Clarke subdifferential
58C06
parabolic-parabolic system
49J52
hyperbolic-parabolic system
47H05
93C20
existence result
47H04
ISSN:1439-8516, 1439-7617
Online Access:Get full text
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Summary: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 ).
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-023-2065-2