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MiS Preprint
25/2015

Spatially discrete reaction-diffusion equations with discontinuous hysteresis

Pavel Gurevich and Sergey Tikhomirov

Abstract

We deal with a class of lattice dynamical systems, namely hysteretic reaction-diffusion equations that are continuous in time and discrete in space. Our primary goal is to analyze a new mechanism that leads to appearance of a spatio-temporal pattern called rattling. The rattling is characterized by a specific behavior of the solution profile: while evolving in time, it oscillates up- and downwards and "switches" hysteresis at nodes satisfying a certain rule. In the one-dimensional case, this switching rule makes the profile shape two hills propagating outwards the origin with decreasing velocity. In a prototype case, we prove the existence of rattling and identify the propagation velocity.

Received:
15.04.2015
Published:
17.04.2015
MSC Codes:
37L60, 34C55, 35B36
Keywords:
spatially distributed hysteresis, lattice dynamical systems, pattern formation, rattling

Related publications

inJournal
2018 Repository Open Access
Pavel Gurevich and Sergey Tikhomirov

Spatially discrete reaction-diffusion equations with discontinuous hysteresis

In: Annales de l'Institut Henri Poincaré / C, 35 (2018) 4, pp. 1041-1077