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Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (4): 515-534.doi: https://doi.org/10.1007/s10483-014-1809-7

• 论文 • 上一篇    

Long time behavior of solutions to coupled Burgers-complex Ginzbury-Landau (Burgers-CGL) equations for flames governed by sequential reaction

郭昌洪1 房少梅1 郭柏灵2   

  1. 1. Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China;
    2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
  • 收稿日期:2012-10-12 修回日期:2013-05-08 出版日期:2014-04-09 发布日期:2014-04-01
  • 通讯作者: Shao-mei FANG, Professor, Ph.D. E-mail:dz90@scau.edu.cn

Long time behavior of solutions to coupled Burgers-complex Ginzbury-Landau (Burgers-CGL) equations for flames governed by sequential reaction

 GUO Chang-Hong, FANG Shao-Mei, GUO Bai-Ling   

  1. 1. Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China;
    2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
  • Received:2012-10-12 Revised:2013-05-08 Online:2014-04-09 Published:2014-04-01
  • Contact: Shao-mei FANG, Professor, Ph.D. E-mail:dz90@scau.edu.cn

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被引次数

6

摘要： This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau (Burgers-CGL) equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.

关键词: boundary layer, wavelength conversion mechazlism, receptivity, T-S wave, coupled Burgers-complex Ginzbury-Landau (Burgers-CGL),  global solution, global attractor, Hausdorff and fractal dimension

Abstract: This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau (Burgers-CGL) equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.

Key words: boundary layer, receptivity, T-S wave, wavelength conversion mechazlism, coupled Burgers-complex Ginzbury-Landau (Burgers-CGL),  global solution, global attractor, Hausdorff and fractal dimension

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