Pulsating traveling waves in the singular limit of a reaction–diffusion system in solid combustion

  • R. Monneau

    Ecole Nationale des Ponts et Chaussées, CERMICS, 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France
  • G.S. Weiss

    Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914 Japan

Abstract

We consider a coupled system of parabolic/ODE equations describing solid combustion. For a given rescaling of the reaction term (the high activation energy limit), we show that the limit solution solves a free boundary problem which is to our knowledge new.

In the time-increasing case, the limit coincides with the Stefan problem with spatially inhomogeneous coefficients. In general it is a parabolic equation with a memory term.

In the first part of our paper we give a characterization of the limit problem in one space dimension. In the second part of the paper, we construct a family of pulsating traveling waves for the limit one phase Stefan problem with periodic coefficients. This corresponds to the assumption of periodic initial concentration of reactant.

Cite this article

R. Monneau, G.S. Weiss, Pulsating traveling waves in the singular limit of a reaction–diffusion system in solid combustion. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 4, pp. 1207–1222

DOI 10.1016/J.ANIHPC.2008.09.002