Communications in Mathematical Sciences

Volume 12 (2014)

Number 8

Global smooth solutions of the generalized KS-CGL equations for flames governed by a sequential reaction

Pages: 1457 – 1474



Changhong Guo (School of Management, Guangdong University of Technology, Guangzhou, China)

Shaomei Fang (Department of Mathematics, South China Agricultural University, Guangzhou, China)

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)


In this paper, we investigate the periodic initial value problem and Cauchy problem of the generalized Kuramoto-Sivashinsky-complex Ginzburg-Landau (GKS-CGL) equations for flames governed by a sequential reaction. We prove the global existence and uniqueness of solutions to these two problems in various spatial dimensions via delicate a priori estimates, the Galerkin method, and so-called continuity method.


global existence, generalized KS-CGL equations, sequential reaction, a priori estimates, Galerkin method

2010 Mathematics Subject Classification

35D35, 35Q56

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