Free boundaries in problems with hysteresis
Analysis of PDEs
2017-03-21 v1
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.
Keywords
Cite
@article{arxiv.1411.5376,
title = {Free boundaries in problems with hysteresis},
author = {D. E. Apushkinskaya and N. N. Uraltseva},
journal= {arXiv preprint arXiv:1411.5376},
year = {2017}
}
Comments
14 pages, 4 figures