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arXiv · 1901.07256

Pulsating solutions for multidimensional bistable and multistable equations

Thomas Giletti·Luca Rossi
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Abstract

We devote this paper to the issue of existence of pulsating travelling front solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In the multistable case, the notion of a single front is not sufficient to understand the dynamics of solutions, and we instead observe the appearance of a so-called propagating terrace. This roughly refers to a finite family of stacked fronts connecting intermediate stable steady states whose speeds are ordered. Surprisingly, for a given equation, the shape of this terrace (i.e., the involved intermediate states or even the cardinality of the family of fronts) may depend on the direction of propagation.

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Thomas Giletti, Luca Rossi. 2019-01-22. Pulsating solutions for multidimensional bistable and multistable equations. https://arxiv.org/abs/1901.07256

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