连串反应中控制火焰的耦合GKS-CGL方程组解的极限行为

本文考虑连串反应中控制火焰的耦合广义Kuramoto Sivashinsky-Ginzburg Landau(GKS-CGL)方程组的周期初值问题,主要研究其解在系数g→0和δ→0时的极限行为.首先,采用Galerkin方法,通过构造一系列精细的先验估计,得到GKS-CGL方程组周期初值问题整体光滑解的存在唯一性.其次,利用一致有界估计证得GKS-CGL方程组极限解收敛,并给出解的收敛率估计.

Limit behavior of the solutions for the GKS-CGL equations for flames governed by a sequential reaction

We study the limit behavior of the solutions of the periodic initial value problem for the GKS-CGL equations for flames governed by a sequential reaction as the parameters g → 0 and δ →0. Firstly the existence and uniqueness of the smooth solutions for the GKS-CGL equations are obtained through delicate a priori estimates and the Galerkin method. We also show that the solutions of the GKS-CGL equations converge to the solutions of the Burgers-CGL equations as g → 0 and δ →0. Moreover the optimal convergence rates are given based on the uniformly bounded estimates.