Singular Limit and Homogenization for Flame Propagation in Periodic Excitable Media |
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Authors: | Email author" target="_blank">Luis A?CaffarelliEmail author Ki-Ahm?Lee Antoine?Mellet |
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Institution: | (1) Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA;(2) Seoul National University, Seoul, 151-747, Korea;(3) Laboratoire Mathématiques pour lIndustrie et la Physique, Université P. Sabatier, 118, route de Narbonne, 31062 Toulouse, France |
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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 related to the activation energy. The existence of pulsating travelling fronts for fixed 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 goes to zero (and |L| is fixed), toward a solution of a free boundary problem. |
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