Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities

Abstract
In this paper we address the large-time behavior of solutions of bistable and multistable reaction–diffusion equation 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. (2023). Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities. Nonlinear Analysis: Real World Applications, 74, 103924. https://doi.org/10.1016/j.nonrwa.2023.103924

Acknowledgements
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, France, 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, France via the project Indyana under grant agreement ANR- 21- CE40-0008.

Publisher
Elsevier BV

Journal
Nonlinear Analysis: Real World Applications

DOI
10.1016/j.nonrwa.2023.103924

arXiv
2207.14565

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S1468121823000949

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2023-07-16 10:40:52
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