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Abstract:

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.

Registro:

Documento: Artículo
Título:Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames
Autor:Lederman, C.; Roquejoffre, J.-M.; Wolanski, N.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina
Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
Palabras clave:Combustion; Half derivatives; High activation energies; Linear and nonlinear stability
Año:2004
Volumen:183
Número:2
Página de inicio:173
Página de fin:239
DOI: http://dx.doi.org/10.1007/s10231-003-0085-1
Título revista:Annali di Matematica Pura ed Applicata
Título revista abreviado:Ann. Mat. Pura Appl.
ISSN:03733114
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v183_n2_p173_Lederman

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Citas:

---------- APA ----------
Lederman, C., Roquejoffre, J.-M. & Wolanski, N. (2004) . Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames. Annali di Matematica Pura ed Applicata, 183(2), 173-239.
http://dx.doi.org/10.1007/s10231-003-0085-1
---------- CHICAGO ----------
Lederman, C., Roquejoffre, J.-M., Wolanski, N. "Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames" . Annali di Matematica Pura ed Applicata 183, no. 2 (2004) : 173-239.
http://dx.doi.org/10.1007/s10231-003-0085-1
---------- MLA ----------
Lederman, C., Roquejoffre, J.-M., Wolanski, N. "Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames" . Annali di Matematica Pura ed Applicata, vol. 183, no. 2, 2004, pp. 173-239.
http://dx.doi.org/10.1007/s10231-003-0085-1
---------- VANCOUVER ----------
Lederman, C., Roquejoffre, J.-M., Wolanski, N. Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames. Ann. Mat. Pura Appl. 2004;183(2):173-239.
http://dx.doi.org/10.1007/s10231-003-0085-1