Title

On Systems of Parabolic Variational Inequalities with Multivalued Terms

Abstract

In this paper we present an analytical framework for the following system of multivalued parabolic variational inequalities in a cylindrical domain [Formula] where Kk is a closed and convex subset of [Formula], Ak is a time-dependent quasilinear elliptic operator, and fk: Q x ℝm → 2 is an upper semicontinuous multivalued function with respect to s ∈ ℝm. We provide an existence theory for the above system under certain coercivity assumptions. In the noncoercive case, we establish an appropriate sub-supersolution method that allows us to get existence and enclosure results. As an application, a multivalued parabolic obstacle system is treated. Moreover, under a lattice condition on the constraints Kk, systems of evolutionary variational-hemivariational inequalities are shown to be a subclass of the above system of multivalued parabolic variational inequalities.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Evolutionary variational-hemivariational inequalities; Multivalued parabolic variational inequality; Obstacle problem; Pseudomonotone multivalued operator; Sub-supersolution; System of parabolic variational inequalities; Upper semicontinuous multivalued operator

International Standard Serial Number (ISSN)

0026-9255

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Springer, All rights reserved.

Publication Date

01 Feb 2021

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