Abstract.
This paper is concerned with a class of singular equations modelling the combustion of premixed gases in periodic media. The model involves two parameters: the period of the medium |L| and a singular parameter ɛ related to the activation energy. The existence of pulsating travelling fronts for fixed ɛ and |L| was proved by Berestycki & Hamel in [BH]. In the present paper, we investigate the behaviour of such solutions when More precisely, we establish that pulsating travelling fronts behave like travelling waves, when the period |L| is small and . We also study the convergence of the solution, as ɛ goes to zero (and |L| is fixed), toward a solution of a free boundary problem.
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L.C. Evans
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Caffarelli, L., Lee, KA. & Mellet, A. Singular Limit and Homogenization for Flame Propagation in Periodic Excitable Media. Arch. Rational Mech. Anal. 172, 153–190 (2004). https://doi.org/10.1007/s00205-003-0299-9
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DOI: https://doi.org/10.1007/s00205-003-0299-9