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

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• 作者：Chang-hong Guo (1)
  Shao-mei Fang (1)
  Bo-ling Guo (2)
  
• 关键词：coupled Burgers ; complex Ginzbury ; Landau (Burgers ; CGL) ; global solution ; global attractor ; Hausdorff and fractal dimension ; O175.2 ; 35B41 ; 37L30 ; 35D35
• 刊名：Applied Mathematics and Mechanics
• 出版年：2014
• 出版时间：April 2014
• 年：2014
• 卷：35
• 期：4
• 页码：515-534
• 全文大小：236 KB
• 参考文献：1. Williams, F. A. / Combustion Theory, Benjamin Cummings, Menlo Park (1985)
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• 作者单位：Chang-hong Guo (1)
  Shao-mei Fang (1)
  Bo-ling Guo (2)
  
  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
  
• ISSN：1573-2754

文摘

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.