Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recent Advances in Reaction-Diffusion Equations with Non-Ideal Relays   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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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
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The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat