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-sca...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 chem- ical 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.展开更多
In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term ｜P｜2σP is replaced with the genera...In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term ｜P｜2σP is replaced with the generalized form ｜P｜2P, see [18]. The main novelty compared with [18] in this paper is to control the norms of the first order of the solutions and extend the global well-posedness to three dimensional space.展开更多
基金supported by the National Natural Science Foundation of China(No.11271141)
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 chem- ical 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.
文摘In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term ｜P｜2σP is replaced with the generalized form ｜P｜2P, see [18]. The main novelty compared with [18] in this paper is to control the norms of the first order of the solutions and extend the global well-posedness to three dimensional space.
