Communications in Mathematical Sciences
Volume 12 (2014)
Global smooth solutions of the generalized KS-CGL equations for flames governed by a sequential reaction
Pages: 1457 – 1474
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