Free boundaries in problems with hysteresis

Here, 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...

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Published inPhilosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 373; no. 2050; p. 20140271
Main Authors Apushkinskaya, D. E., Uraltseva, N. N.
Format Journal Article
LanguageEnglish
Published England The Royal Society Publishing 13.09.2015
Subjects
Algorithms
Animals
Computer Simulation
Free Boundary
Humans
Models, Biological
Models, Chemical
Non-Ideal Relay
Nonlinear Dynamics
Regularity
non-ideal relay
regularity
free boundary
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Summary:Here, 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 with sufficiently large q. Several open problems in this direction are proposed as well.
Bibliography:Theme issue ‘Free boundary problems and related topics’ compiled and edited by Henrik Shahgholian, Gui-Qiang Chen and Juan Luis Vázquez
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One contribution of 15 to a theme issue ‘Free boundary problems and related topics’.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2014.0271