On the delay differential variational inequalities of parabolic-elliptic type

In this work, we consider a model of functional differential variational inequalities formulated by a delay differential inclusion and an elliptic variational inequality in Banach spaces. We prove the global solvability of the problem and we have given some sufficient conditions to ensure the existe...

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Published inComplex variables and elliptic equations Vol. 67; no. 12; pp. 3048 - 3073
Main Authors Thi Van Anh, Nguyen, Thuy, Tran Van
Format Journal Article
LanguageEnglish
Published Colchester Taylor & Francis 02.12.2022
Taylor & Francis Ltd
Subjects
Banach spaces
decay solutions
Differential variational inequalities
elliptic variational inequalities
fixed point theory
global attractors
Inclusions
Inequalities
measure of noncompactness
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Summary:In this work, we consider a model of functional differential variational inequalities formulated by a delay differential inclusion and an elliptic variational inequality in Banach spaces. We prove the global solvability of the problem and we have given some sufficient conditions to ensure the existence of decay solutions. Moreover, the existence of a global attractor for the semiflow governed by our system is presented thanks to the framework of Melnik and Valero [On attractors of multivalued semi-flows and differential inclusions. Set-Valued Anal. 1998;6:83-111]. The application to partial differential inclusions driven by obstacle constraints is given to illustrate our abstract results.
ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2021.1968382