Free boundaries in problems with hysteresis

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 $W_q^{2,1}$ with sufficiently large $q$. Several open problems in this direction are proposed as well.

14 pages, 4 figures

References in corpus (4)

• Reaction-diffusion equations with spatially distributed hysteresis
• Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis
• On regularity properties of solutions to the hysteresis-type problems
• Spatially discrete reaction-diffusion equations with discontinuous hysteresis

Cited by in corpus (3)

• Free Boundary Problems: The Forefront of Current and Future Developments
• Spatially discrete reaction-diffusion equations with discontinuous hysteresis
• Rattling in spatially discrete diffusion equations with hysteresis