On Systems of Parabolic Variational Inequalities with Multivalued Terms

Author

Siegfried Carl
Vy Khoi Le, Missouri University of Science and TechnologyFollow

Abstract

In this paper we present an analytical framework for the following system of multivalued parabolic variational inequalities in a cylindrical domain [Formula] where K_k is a closed and convex subset of [Formula], A_k is a time-dependent quasilinear elliptic operator, and f_k: Q x ℝ^m → 2^ℝ is an upper semicontinuous multivalued function with respect to s ∈ ℝ^m. 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 K_k, systems of evolutionary variational-hemivariational inequalities are shown to be a subclass of the above system of multivalued parabolic variational inequalities.

Recommended Citation

S. Carl and V. K. Le, "On Systems of Parabolic Variational Inequalities with Multivalued Terms," Monatshefte fur Mathematik, vol. 194, no. 2, pp. 227 - 260, Springer, Feb 2021.

The definitive version is available at https://doi.org/10.1007/s00605-020-01477-6

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