Asymptotic behavior of solutions to a class of coupled semilinear parabolic systems with gradient terms

This paper concerns the asymptotic behavior of solutions to the Cauchy problem of a class of coupled semilinear parabolic systems with gradient terms. Using the energy comparison method and comparison principle, the blow-up theorem of Fujita type is established and the critical Fujita curve is formulated by spacial dimension, the behavior of the coefficient of the gradient term at infinity.