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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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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paper:paper_03733114_v183_n2_p173_Lederman2023-06-08T15:37:52Z Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames Lederman, Claudia Beatriz Wolanski, Noemi Irene Combustion Half derivatives High activation energies Linear and nonlinear stability 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. Fil:Lederman, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2004 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 |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Combustion Half derivatives High activation energies Linear and nonlinear stability |
| spellingShingle |
Combustion Half derivatives High activation energies Linear and nonlinear stability Lederman, Claudia Beatriz Wolanski, Noemi Irene Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| topic_facet |
Combustion Half derivatives High activation energies Linear and nonlinear stability |
| description |
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. |
| author |
Lederman, Claudia Beatriz Wolanski, Noemi Irene |
| author_facet |
Lederman, Claudia Beatriz Wolanski, Noemi Irene |
| author_sort |
Lederman, Claudia Beatriz |
| title |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_short |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_full |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_fullStr |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_full_unstemmed |
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| title_sort |
mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames |
| publishDate |
2004 |
| url |
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 |
| work_keys_str_mv |
AT ledermanclaudiabeatriz mathematicaljustificationofanonlinearintegrodifferentialequationforthepropagationofsphericalflames AT wolanskinoemiirene mathematicaljustificationofanonlinearintegrodifferentialequationforthepropagationofsphericalflames |
| _version_ |
1768545420727812096 |