数学物理学报(英文版) ›› 1991, Vol. 11 ›› Issue (3): 254-266.
丁夏畦, 赵会江
Ding Xiaxi, Zhao Huijiang
摘要： In this paper, we are concerned with the Cauchy problem:
ut=△u+|u|γ-1u-u x∈Rn,γ>1,t∈R+ u(x,0)=u0(x) in Dqα. We got some existence and asymptotic results of their global solutions. Additionally, we got the global existence theorem of the Cauchy problem
ut=△u+|u|γ-1u x∈Rn,γ>1,t∈R+ u(x,0)=u0(x) in Dqα, where q∈[(1)/2n(γ-1),∞),α=(2)/γ-1-(n)/q, in the case(1)/2n(γ-1)>1.