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arXiv · 1508.02233

Recent Advances in Reaction-Diffusion Equations with Non-Ideal Relays

Mark Curran·Pavel Gurevich·Sergey Tikhomirov
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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.

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Mark Curran, Pavel Gurevich, Sergey Tikhomirov. 2015-08-10. Recent Advances in Reaction-Diffusion Equations with Non-Ideal Relays. https://arxiv.org/abs/1508.02233

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