Convergence to a terrace solution in multistable reaction-diffusion equations with discontinuities
KAUST DepartmentComputer, 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
Permanent link to this recordhttp://hdl.handle.net/10754/687422
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AbstractIn 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.
CitationGiletti, 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
SponsorsThis 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.