English

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 Wq2,1W^{2,1}_q with sufficiently large qq. 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

R2 v1 2026-06-22T07:05:10.823Z