Abstract: By using the method of energy estimates and the comparison principle, we studied the long time asymptotic behavior of solutions to the Cauchy problems of a class of coupled semilinear diffusion systems with firstorder terms. We gave the Fujita critical curves which described the global existence and blowup properties of solutions, and established the theorems of Fujita type.

Key words: coupled diffusion systems, Fujita critical curve, theorem of Fujita type