Multi-dimensional traveling fronts in bistable reaction-diffusion equations

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49 Citations (Scopus)


This paper studies traveling front solutions of convex polyhedral shapes in bistable reaction-diffusion equations including the Allen-Cahn equations or the Nagumo equations. By taking the limits of such solutions as the lateral faces go to in finity, we construct a three-dimensional traveling front solution for any given g ε C (S 1) with min0≤θ2≤ π g(θ) = 0.

Original languageEnglish
Pages (from-to)1011-1046
Number of pages36
JournalDiscrete and Continuous Dynamical Systems
Issue number3
Publication statusPublished - Mar 2012
Externally publishedYes


  • Allen-Cahn equation
  • Multi-dimensional wave.
  • Traveling wave

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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