GLOBAL SOLUTION OF A SEMILINEAR PARABOLIC EQUATION~*

In this paper, we are concerned with the Cauchy problem:in D_q~α. We got some existence and asymptotic results of their global solutions. Additionally, we got the global existence theorem of the Cauchy problemin D_q~α, where q∈(1/2)n(γ-1),∞),α=(2/γ-1)-(n/q), in the case(1/2)n(γ-1)>1.