Rattling in spatially discrete diffusion equations with hysteresis

Pavel Gurevich and Sergey Tikhomirov

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Submission date: 21. Jan. 2016
Pages: 26
published in: Multiscale modeling and simulation, 15 (2017) 3, p. 1176-1197 
DOI number (of the published article): 10.1137/16M106039X
Bibtex
MSC-Numbers: 34K31, 47J40, 35B36, 37L60
Keywords and phrases: Spatially discrete parabolic equations, reaction-diffusion equations, lattice, hysteresis, pattern, rattling
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Abstract:
The paper treats a reaction-diffusion equation with hysteretic nonlinearity on a one-dimensional lattice. It arises as a result of the spatial discretization of the corresponding continuous model with so-called nontransverse initial data and exhibits a propagating microstructure — which we call rattling — in the hysteretic component of the solution. We analyze this microstructure and determine the speed of its propagation depending on the parameters of hysteresis and the nontransversality coefficient in the initial data.