Parabolic Quasi-Variational Inequalities (I) -- Semimonotone Operator Approach
Analysis of PDEs
2020-10-06 v2
Abstract
Variational inequalities, formulated on unknown dependent convex sets, are called quasi-variational inequalities (QVI). This paper is concerned with the abstract approach to a class of parabolic QVIs arising in many biochemical/mechanical problems, based on a compactness theorem for parabolic variational inequalities (cf. [9]). The prototype of our model for QVIs of parabolic type is formulated in a reflexive Banach space as the sum of the time-derivative operator under unknown convex constraints and a semimonotone operator, including a feedback system which selects a convex constraint. The main objective of this work is to specify a class of unknown-state dependent convex constraints and to give a precise formulation of QVIs.
Keywords
Cite
@article{arxiv.2009.14129,
title = {Parabolic Quasi-Variational Inequalities (I) -- Semimonotone Operator Approach},
author = {Maria Gokieli and Nobuyuki Kenmochi and Marek Niezgódka},
journal= {arXiv preprint arXiv:2009.14129},
year = {2020}
}