Free boundaries in problems with hysteresis
D.E. Apushkinskaya, N.N. Uraltseva
TL;DR
This paper surveys parabolic free boundary problems involving hysteresis operators, focusing on the structure of free boundaries and properties of strong solutions in biological and chemical processes with memory effects.
Contribution
It provides a comprehensive overview of free boundary problems with hysteresis, highlighting the structure of free boundaries and properties of strong solutions, and proposes open problems.
Findings
Analysis of free boundary structures in hysteresis problems
Properties of strong solutions in Sobolev spaces
Identification of open research questions
Abstract
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 with sufficiently large . Several open problems in this direction are proposed as well.
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