Recent Advances in Reaction-Diffusion Equations with Non-Ideal Relays
Analysis of PDEs
2015-08-11 v1
Abstract
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and solutions. We assert that the equation with transverse initial data possesses a unique solution, which remains transverse for some time, and also describe its regularity. At a moment when the solution becomes nontransverse, we discretize the spatial variable and analyze the resulting lattice dynamical system with hysteresis. In particular, we discuss a new pattern formation mechanism --- {\it rattling}, which indicates how one should reset the continuous model to make it well posed.
Cite
@article{arxiv.1508.02233,
title = {Recent Advances in Reaction-Diffusion Equations with Non-Ideal Relays},
author = {Mark Curran and Pavel Gurevich and Sergey Tikhomirov},
journal= {arXiv preprint arXiv:1508.02233},
year = {2015}
}
Comments
24 pages, 12 figures