Free boundaries in problems with hysteresis

In this note we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes "with memory" in which various substances interact according to hysteresis law. Our main objective is to disc...

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Bibliographic Details
Published inarXiv.org
Main Authors Apushkinskaya, D E, Uraltseva, N N
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.11.2014
Subjects
Biological activity
Chemical reactions
Free boundaries
Hysteresis
Mathematics - Analysis of PDEs
Organic chemistry
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Summary:In this note we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes "with memory" in which various substances interact according to hysteresis law. Our main objective is to discuss the structure of the free boundaries and the properties of the so-called "strong solutions" belonging to the anisotropic Sobolev class \(W^{2,1}_q\) with sufficiently large \(q\). Several open problems in this direction are proposed as well.
ISSN:2331-8422
DOI:10.48550/arxiv.1411.5376