Rossiyskiy Vestnik Perinatologii i Pediatrii.
National Academy of Pediatric Science and Innovation.
Vol. 62.
2017.
P. 21-28
Rattling in spatially discrete diffusion equations with hysteresis
The paper treats a reaction-diffusion equation with hysteretic nonlinearity on a onedimensional 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. © 2017 Society for Industrial and Applied Mathematics.
Authors
Gurevich P.
1,
2
,
Tikhomirov S.3,
4
Publisher
Society for Industrial and Applied Mathematics Publications
Number of issue
3
Language
English
Pages
1176-1197
Status
Published
Link
Volume
15
Year
2017
Organizations
- 1 Free University of Berlin, Institute of Mathematics i, Arnimalle 3, Berlin, 14195, Germany
- 2 Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
- 3 St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russian Federation
- 4 Max Planck Institute for Mathematics in the Sciences, Inselstraé 22, Leipzig, 04103, Germany
Keywords
Hysteresis; Lattice; Pattern; Rattling; Reaction-diffusion equations; Spatially discrete parabolic equations
Date of creation
19.10.2018
Date of change
19.10.2018
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Proceedings - 31st European Conference on Modelling and Simulation, ECMS 2017.
European Council for Modelling and Simulation.
2017.
P. 701-705