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Quenching and Propagation in KPP Reaction-Diffusion Equations with a Heat Loss

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Abstract.

We consider a reaction-diffusion system of KPP type in a shear flow and with a non-zero heat-loss parameter. We establish criteria for the flame blow-off and propagation, and identify the propagation speed in terms of the exponential decay of the initial data. We prove the existence of travelling fronts for all speeds c>max(0,c*) in the case Le=1, where c* ∈ ℝ. This seems to be one of the first non-perturbative results on the existence of fronts for the thermo-diffusive system in higher dimensions.

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Authors and Affiliations

  1. EHESS, CAMS, 54 Boulevard Raspail, F-75006, Paris, France

    Henri Berestycki

  2. Faculté Saint-Jérôme Case Cour A, Université Aix-Marseille III LATP, Avenue Escadrille Normandie-Niemen, F-13397, Marseille Cedex 20, France

    Francois Hamel

  3. Department of Mathematics, University of Wisconsin Madison, WI, 53706, USA

    Alexander Kiselev

  4. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Lenya Ryzhik

Authors
  1. Henri Berestycki
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  2. Francois Hamel
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  3. Alexander Kiselev
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  4. Lenya Ryzhik
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Corresponding author

Correspondence to Lenya Ryzhik.

Additional information

Communicated by P. H. Rabinowitz

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Berestycki, H., Hamel, F., Kiselev, A. et al. Quenching and Propagation in KPP Reaction-Diffusion Equations with a Heat Loss. Arch. Rational Mech. Anal. 178, 57–80 (2005). https://doi.org/10.1007/s00205-005-0367-4

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  • DOI: https://doi.org/10.1007/s00205-005-0367-4

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