Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames

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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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Autor principal: Lederman, C.
Otros Autores: Roquejoffre, J.-M, Wolanski, N.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2004
Materias:
COMBUSTION
Acceso en línea:Registro en Scopus
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100 1 |a Lederman, C. 
245 1 0 |a Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames 
260 |c 2004 
270 1 0 |m Lederman, C.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina; email: clederma@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Audounet, J., Giovangigli, V., Roquejoffre, J.-M., A threshold phenomenon in the propagation of a point source initiated flame (1998) Physica D, 121, pp. 295-316 
504 |a D'Angelo, Y., Joulin, G., Collective effects and dynamics of non-adiababtic flame balls (2001) Combust. Theory Model., 5, pp. 1-20 
504 |a Audounet, J., Roquejoffre, J.-M., Rouzaud, H., Numerical simulation of a point-source initiated flame ball with heat losses (2002) M2AN, Math. Model. Numer. Anal., 36, pp. 273-291 
504 |a Berestycki, H., Nicolaenko, B., Scheurer, B., Travelling wave solutions to combustion models and their singular limits (1985) SIAM J. Math. Anal., 16, pp. 1207-1242 
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504 |a Buckmaster, J.D., Joulin, G., Radial propagation of premixed flames and √ behaviour (1989) Combust. Flame, 78, pp. 275-286 
504 |a Buckmaster, J.D., Joulin, G., Ronney, P., The effects of radiation on flame balls at zero gravity (1990) Combust. Flame, 79, pp. 381-392 
504 |a Caffarelli, L.A., Vázquez, J.-L., A free-boundary problem for the heat equation arising in flame propagation (1995) Trans. Am. Math. Soc., 347, pp. 411-441 
504 |a Caffarelli, L.A., Lederman, C., Wolanski, N., Uniform estimates and limits for a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J., 46, pp. 453-489 
504 |a Caffarelli, L.A., Lederman, C., Wolanski, N., Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J., 46, pp. 719-740 
504 |a Fernandez Bonder, J., Wolanski, N., A free-boundary problem in combustion theory (2000) Interfaces Free Bound., 2, pp. 381-1111 
504 |a Gidas, B., Ni, W.-M., Nirenberg, L., Symmetry and related properties via the maximum principle (1979) Commun. Math. Phys., 68, pp. 209-243 
504 |a Glangetas, L., Etude d'une limite singulière d'un modèle intervenant en combustion (1992) Asymptotic Anal., 5, pp. 317-342 
504 |a Glangetas, L., Roquejoffre, J.-M., Bifurcations of travelling waves in the thermo-diffusive model for flame propagation (1996) Arch. Ration. Mech. Anal., 134, pp. 341-402 
504 |a Grenier, E., Rousset, F., Stability of one-dimensional boundary layers by using Green's functions (2001) Commun. Pure Appl. Math., 53, pp. 1343-1385 
504 |a Henry, D., Geometric theory of semilinear parabolic equations (1981) Lect. Notes Math., , New York: Springer 
504 |a Joulin, G., Point-source initiation of lean spherical flames of light reactants: An asymptotic theory (1985) Combust. Sci. Tech., 43, pp. 99-113 
504 |a Joulin, G., Preferential diffusion and the initiation of lean flames of light fuels (1987) SIAM J. Appl. Math., 47, pp. 998-1016 
504 |a Joulin, G., Cambray, P., Jaouen, N., On the response of a flame ball to oscillating velocity gardients (2002) Combust. Theory Model., 6, pp. 53-78 
504 |a Ladyzhenskaya, O.A., Uraltseva, N.N., Solonnikov, V.A., Linear and quasilinear equations of parabolic type (1968) Transi. Math. Monogr., 23. , Providence: Am. Math. Soc 
504 |a Lederman, C., Roquejoffre, J.-M., Wolanski, N., Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames (2002) C. R. Acad. Sci., Paris, Sér. I, Math., 334, pp. 569-574 
504 |a Pazy, A., Semigroups of linear operators and applications to partial differential equations (1983) Appli. Math. Sci., 44. , New York: Springer 
504 |a Rouzaud, H., Dynamique d'un modèle intégre-différentiel de flamme sphérique avec pertes de chaleur (2001) C. R. Acad. Sci., Paris, sér I, Math., 332, pp. 1083-1086 
504 |a Zeldovich, Ya.B., Barenblatt, G.I., Librovich, V.B., Makhviladze, G.M., (1985) The Mathematical Theory of Combustion and Explosions, , New York: Consult. Bureau 
504 |a Zumbrun, K., Howard, P., Pointwise semigroup methods and stability of viscous shock waves (1998) Indiana Univ. Math. J., 47, pp. 741-871 
520 3 |a 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.  |l eng 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina 
593 |a Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France 
650 1 7 |2 spines  |a COMBUSTION 
690 1 0 |a HALF DERIVATIVES 
690 1 0 |a HIGH ACTIVATION ENERGIES 
690 1 0 |a LINEAR AND NONLINEAR STABILITY 
700 1 |a Roquejoffre, J.-M. 
700 1 |a Wolanski, N. 
773 0 |d 2004  |g v. 183  |h pp. 173-239  |k n. 2  |p Ann. Mat. Pura Appl.  |x 03733114  |w (AR-BaUEN)CENRE-1530  |t Annali di Matematica Pura ed Applicata 
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856 4 0 |u https://doi.org/10.1007/s10231-003-0085-1  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_03733114_v183_n2_p173_Lederman  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v183_n2_p173_Lederman  |y Registro en la Biblioteca Digital 
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