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Monotonicity of Bistable Transition Fronts in ℝN

Journal of Elliptic and Parabolic Equations volume 2, pages 145–155 (2016)Cite this article

Abstract

This paper is concerned with the monotonicity of transition fronts for bistable reaction diffusion equations. Transition fronts generalize the standard notions of traveling fronts. Known examples of standard traveling fronts are the planar fronts and the fronts with conical-shaped or pyramidal level sets which are invariant in a moving frame. Other more general non-standard transition fronts with more complex level sets were constructed recently. In this paper, we prove the time monotonicity of all bistable transition fronts with non-zero global mean speed, whatever shape their level sets may have.

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Authors and Affiliations

  1. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

    Hongjun Guo & François Hamel

Authors
  1. Hongjun Guo
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  2. François Hamel
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Corresponding author

Correspondence to Hongjun Guo.

Additional information

Dedicated to Professor David Kinderlehrer

This work has been carried out thanks to the support of the A*MIDEX project (no ANR-11-IDEX-0001-02) and Archimède Labex (no ANR-11-LABX-0033) funded by the “Investissements d’Avenir” French Government program, managed by the French National Research Agency (ANR). The research leading to these results has also received funding from the ANR within the project NONLOCAL (no ANR-14-CE25-0013) and from the European Research Council under the European Unions Seventh Framework Programme(FP/2007-2013) / ERC Grant Agreement n.321186 - ReaDi - Reaction- Diffusion Equations, Propagation and Modelling.

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Cite this article

Guo, H., Hamel, F. Monotonicity of Bistable Transition Fronts in ℝN. J Elliptic Parabol Equ 2, 145–155 (2016). https://doi.org/10.1007/BF03377398

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  • DOI: https://doi.org/10.1007/BF03377398

2010 Mathematics Subject Classication

  • Primary: 35B08, 35C07, 35K57
  • Secondary: 35B45

Key words and phrases

  • Reaction-diffusion equations
  • Transition fronts
  • Monotonicity