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Pulsating solutions for multidimensional bistable and multistable equations

  • Thomas Giletti
  • Luca RossiEmail author
Article
  • 4 Downloads

Abstract

We investigate the existence of pulsating front-like 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.

Notes

Acknowledgements

This study was funded by European Research Council (No. 321186) and Agence Nationale de la Recherche (No. ANR-14-CE25-0013).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Univ. Lorraine, IECL UMR 7502Vandoeuvre-lès-NancyFrance
  2. 2.CNRS, EHESS, CAMSParisFrance

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