一类非线性耦合对流扩散方程组的临界Fujita曲线

Critical Fujita Curves for a Class of Nonlinear Coupled Convection-Diffusion Systems

用能量估计方法和比较原理建立一类非线性耦合对流扩散方程组的齐次Neumann外区域问题的Fujita型定理,确定刻画解整体是否存在的临界Fujita曲线,并刻画空间维数及方程组中对流项和反应项对解长时间渐近行为的影响。

We used the method of energy estimate and the comparison principle to establish the theorem of Fujita type for the homogeneous Neumann exterior region problems for a class of nonlinear coupled convection-diffusion systems.We determined the critical Fujita curves that described whether solutions existed globally or not,and described the influence of the spacial dimension,convection and reaction terms of the systems on the long-term asymptotic behavior of the solution.