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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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:
Apr 15, 2015
Published:
Apr 17, 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