Convergence to a terrace solution in multistable reaction-diffusion equations with discontinuities

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Type
Preprint
Authors
Giletti, Thomas
Kim, Ho-Youn
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering Division, 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia.
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Date
2022-11-21
Permanent link to this record
http://hdl.handle.net/10754/687422

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Abstract
In this paper we address the large-time behavior of solutions of bistable and multistable reaction-diffusion equations with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case.
Citation
Giletti, T., & Kim, H.-Y. (2022). Convergence to a terrace solution in multistable reaction-diffusion equations with discontinuities (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2207.14565
Sponsors
This work was carried out in the framework of the CNRS International Research Network “ReaDiNet”. The two authors were also supported by the joint PHC Star project MAP, funded by the French Ministry for Europe and Foreign Affairs and the National Research Foundation of Korea. The first author also acknowledges support from ANR via the project Indyana under grant agreement ANR- 21- CE40-0008.
Publisher
Elsevier
Journal
Nonlinear Analysis: Real World Applications
DOI
https://doi.org/10.48550/arXiv.2207.14565
arXiv
2207.14565
Collections
Preprints; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division