Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames
This paper is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [17]. The paper [17] derives, by means of a three-scale matched asymptotics, starting from the classical thermo-diffusive model with high activation energies, an...
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| Autores principales: | , |
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2004
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v183_n2_p173_Lederman http://hdl.handle.net/20.500.12110/paper_03733114_v183_n2_p173_Lederman |
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| Sumario: | This paper is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [17]. The paper [17] derives, by means of a three-scale matched asymptotics, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis Number - i.e. the ratio between thermal and molecular diffusion - to be strictly less than unity. If ε is the inverse of the - reduced activation energy, the idea underlying the construction of [17] is that (i) the time scale of the radius motion is ε-2, and that (ii) at each time step, the solution is ε-close to a steady solution. In this paper, we give a rigorous proof of the validity of this model under the restriction that the Lewis number is close to 1 - independently of the order of magnitude of the activation energy. The method used comprises three steps: (i) a linear stability analysis near a steady - or quasi-steady - solution, which justifies the fact that the relevant time scale is ε-2; (ii) the rigorous construction of an approximate solution; (iii) a nonlinear stability argument. |
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