Abstract: 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.

Key words: critical Fujita curve, theorem of Fujita type, energy estimate, comparison principle