Ya Cheng LIU(1),Hong Xue XIN(2
This paper studies the initial value problem of Reaction-Diffusion system of Fujita type: ut - △u = a1u~α1-12u + b1v~β1-1v, vt - △v = a2u~α2-1u + b2v~β2-1v, u(x,0) = uo(x), v(x,0) = vo(x), (x,t) E R~N x R~+, where ai,bi≥ 0, on,αiβi≥ 1 (i = 1, 2), gives a series of sufficient conditions of the existence and nonexistence of the nonnegative global L~P solutions and classical solutions, and discusses the asymptotic behavior of solutions. The method used in this paper and obtained results are completly different from previous works [1-4], this paper not only generalies the results of [1-5], but also improves the results of [1] on some respect.