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 structure of the free boundaries and the properties of the so-called 'strong solutions' belonging to the anisotropic Sobolev class [Formula: see text] with sufficiently large q. Several open problems in this direction are proposed as well.
Department of Mathematics, Saarland University, PO Box 151150, Saarbrücken 66041, Germany Faculty of Mathematics and Mechanics, St Petersburg State University, Universitetskii pr. 28, St Petersburg 198504, Russia darya@math.uni-sb.de.
D E
http://orcid.org/0000-0002-7743-1998
DE
Apushkinskaya
Faculty of Mathematics and Mechanics, St Petersburg State University, Universitetskii pr. 28, St Petersburg 198504, Russia.
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http://orcid.org/0000-0003-4154-1666
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Uraltseva
D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D008956:Models, Chemical; D017711:Nonlinear Dynamics
free boundary; non-ideal relay; regularity