Reaction-diffusion equations with spatially distributed hysteresis
Analysis of PDEs
2014-04-17 v1
Abstract
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which diffusive and nondiffusive substances interact according to hysteresis law. We find sufficient conditions that guarantee the existence and uniqueness of solutions as well as their continuous dependence on initial data.
Cite
@article{arxiv.1205.3580,
title = {Reaction-diffusion equations with spatially distributed hysteresis},
author = {Pavel Gurevich and Roman Shamin and Sergey Tikhomirov},
journal= {arXiv preprint arXiv:1205.3580},
year = {2014}
}
Comments
30 pages, 14 figures