A class of generalized evolutionary problems driven by variational inequalities and fractional operators

doi:10.1007/s11228-018-0502-7

A class of generalized evolutionary problems driven by variational inequalities and fractional operators

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A class of generalized evolutionary problems driven by variational inequalities and fractional operators

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Bibliographic description

punktacja MEiN [2019]: 70

title:	A class of generalized evolutionary problems driven by variational inequalities and fractional operators
author:	Migórski Stanisław , Zeng Shengda
journal title:	Set-Valued and Variational Analysis
volume:	27
issue:	4
date of publication :	2019
pages:	949-970
ISSN:	1877-0533
eISSN:	1877-0541
DOI:	10.1007/s11228-018-0502-7
language:	English
journal language:	English
abstract in English:	This paper is devoted to a generalized evolution system called fractional partial differential variational inequality which consists of a mixed quasi-variational inequality combined with a fractional partial differential equation in a Banach space. Invoking the pseudomonotonicity of multivalued operators and a generalization of the Knaster-Kuratowski-Mazurkiewicz theorem, first, we prove that the solution set of the mixed quasi-variational inequality involved in system is nonempty, closed and convex. Next, the measurability and upper semicontinuity for the mixed quasi-variational inequality with respect to the time variable and state variable are established. Finally, the existence of mild solutions for the system is delivered. The approach is based on the theory of operator semigroups, the Bohnenblust-Karlin fixed point principle for multivalued mappings, and theory of fractional operators.
keywords in English:	fractional partial differential variational inequalities, Caputo derivative, Knaster-Kuratowski-Mazurkiewicz theorem, Bohnenblust-Karlin fixed point principle, $\phi$-pseudomonotonicity, mixed quasi-variational inequalities
affiliation:	Wydział Matematyki i Informatyki : Katedra Teorii Optymalizacji i Sterowania
type:	journal article
subtype:	academic paper