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arXiv · 2207.14565

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

Thomas Giletti·Ho-Youn Kim
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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.

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Thomas Giletti, Ho-Youn Kim. 2022-07-29. Convergence to a terrace solution in multistable reaction-diffusion equations with discontinuities. https://arxiv.org/abs/2207.14565

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