Abstract

In this paper we study multi-valued parabolic variational inequalities involving quasilinear parabolic operators, and multi-valued integral terms over the underlying parabolic cylinder as well as over parts of the lateral parabolic boundary, where the multi-valued functions involved are assumed to be upper semicontinuous only. Note, since lower semicontinuous multi-valued functions allow always for a Carathéodory selection, this case can be considered as the trivial case and therefore will be omitted. Our main goal is threefold: First, we provide an analytical framework and an existence theory for the problems under consideration. Unlike in recent publications on multi-valued parabolic variational inequalities, the closed convex set K representing the constraints is not required to possess a nonempty interior. Second, we prove enclosure and comparison results based on a recently developed sub-super solution method due to the authors. Third, we consider classes of relevant generalized parabolic variational-hemivariational inequalities that will be shown to be special cases of the multi-valued parabolic variational inequalities under consideration.

Department(s)

Mathematics and Statistics

Publication Status

Open Access

Keywords and Phrases

Comparison principle; Parabolic variational inequality; Pseudomonotone multi-valued operator; Sub-supersolution; Upper semicontinuous multi-valued operator; Variational-hemivariational inequality

International Standard Serial Number (ISSN)

1536-1365

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 The Authors, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Jan 2014

Download

Full Text Link

Share

 
COinS