Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders

P. V. Gordon, C. B. Muratov, M. Novaga

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show that these are, in fact, the only traveling front solutions in the considered problems for sufficiently large speeds. In addition, we show that other traveling fronts connecting to the unstable equilibrium may exist in a certain range of the wave speed. These results are obtained with the help of a variational characterization of such solutions.

Original languageEnglish (US)
Pages (from-to)683-709
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Volume47
Issue number3-4
DOIs
StatePublished - Jul 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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