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Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation
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摘要 The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation. A third-order, fully nonlinear, self-consistent equation for the flame front is derived. Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation. Numerical results which illustrate the dynamics are presented. The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation. A third-order, fully nonlinear, self-consistent equation for the flame front is derived. Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation. Numerical results which illustrate the dynamics are presented.
作者 Claude-Michel BRAUNER Lina HU Luca LORENZI
机构地区 School of Mathematical Sciences Institut de Mathématiques de Bordeaux Dipartimento di Matematica e Informatica
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2013年第1期65-88,共24页 数学年刊（B辑英文版）
基金 Project supported by a grant from the Fujian Administration of Foreign Expert Affairs,China (No.SZ2011008)
关键词 KURAMOTO-SIVASHINSKY方程 燃烧模型 渐近分析 成气 三阶非线性 燃烧过程 方程推导 渐近方法 Asymptotics, Free interface, Kuramoto-Sivashinsky equation, Pseudo-differential operator, Spectral method
分类号 O643.21 [理学—物理化学]
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  • 1Claude-Michel Brauner,Alessandra Lunardi.Instabilities in a Two-Dimensional Combustion Model with Free Boundary[J]. Archive for Rational Mechanics and Analysis . 2000 (2)
  • 2Brauner, C -M,Frankel, M. L,Hulshof, J,Sivashinsky, G. I.Weakly nonlinear asymptotic of the κ-θ model of cellular ?ames: the Q-S equation. Interfaces Free Bound . 2005
  • 3Brauner, C -M,Hulshof, J,Lorenzi, L.Stability of the travelling wave in a 2D weakly nonlinear Stefan problem. Kinetic Related Models . 2009
  • 4Brauner, C.-M,Hulshof, J,Lorenzi, L.Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem. .
  • 5Brauner, C -M,Hulshof, J,Lorenzi, L,Sivashinsky, G. I.A fully nonlinear equation for the ?ame front in a quasi-steady combustion model. Discrete Contin. Dyn. Syst. Ser. A . 2010
  • 6Carvalho, A. N,Cholewa, J. W.Strongly damped wave equations in W1,p(?) × Lp(?). Discrete Contin. Dyn. Syst . 2007
  • 7Frankel, M. L,Gordon, P,Sivashinsky, G. I.A stretch-temperature model for ?ame-?ow interaction. Physics Letters . 2007
  • 8Lorenzi,L.Regularity and analyticity in a two-dimensional combustion model. Adv. Di?erential Equa- tions . 2002
  • 9Lorenzi,L.A free boundary problem stemmed from combustion theory, I, Existence, uniqueness and regularity results. Journal of Mathematical Analysis and Applications . 2002
  • 10Lorenzi,L.A free boundary problem stemmed from combustion theory, II, Stability, instability and bifurcation results. Journal of Mathematical Analysis and Applications . 2002
Chinese Annals of Mathematics,Series B
2013年 第1期

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