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arXiv · 2009.14129

Parabolic Quasi-Variational Inequalities (I) -- Semimonotone Operator Approach

Maria Gokieli·Nobuyuki Kenmochi·Marek Niezgódka
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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.

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Maria Gokieli, Nobuyuki Kenmochi, Marek Niezgódka. 2020-10-05. Parabolic Quasi-Variational Inequalities (I) -- Semimonotone Operator Approach. https://arxiv.org/abs/2009.14129

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