The global solution and nonlinear stability for the coupled CGL–Burgers equations for sequential flames in ℝN

The present paper is devoted to the study of the global solution and nonlinear stability to the coupled complex Ginzburg–Landau and Burgers (CGL–Burgers) equations for sequential flames which describe the interaction of the excited oscillatory and the damped monotonic mode governing a sequential chemical reaction. If the solution blows up in finite time, we derive the lower bound of blow-up rate of blow-up solution.