Fujita型反应扩散方程组整体解的存在性、非存在性与渐近性质

本文研究 Ｆｕｊｉｔａ型反应扩散方程组的初值问题：ｕｔ－△ｕ＝ａ１ｕ~α１－１ｕ＋ｂ１ｖ~β１－１ｖ，ｖｔ－△ｖ＝ａ２ｕ~α２－１ｕ＋ｂ２ｖ~β２－１ｖ，ｕ（Ｘ，０）＝ｕ０（Ｘ），Ｖ（Ｘ，０）＝Ｖ０（Ｘ），（Ｘ，ｔ）Ｒ~Ｎ ｘ Ｒ~＋，其中 ａｉ，ｂｉ≥ ０， αｉ，βｉ≥ １（ｉ＝ １，２），给出了非负整体 Ｌ~ｐ解与古典解存在性与非存在性的一系列充分条件，并讨论了解的渐近性质．本文所用方法和所得结果与已有的工作［１－４］，有很大的不同，不但在某些方面推广了［１－５］，而且从某些方面改进了［１］的结果。

Existence, Nonexistence and Asymptotic Behavior of Global Solutions of Reaction-Diffusion System of Fujita Type

This paper studies the initial value problem of Reaction-Diffusion system ofFujita type:ut- u =a1|u|1-1u+b1|v|1-1v, vt- v = a2|u|2-1u+b2|v|2-1v,u(x,0)=u0(x), v(x,0)=v0(x), (x,t) RN R+,where ai,bi 0, i,i 1 (i=1,2), gives a seriesof sufficient conditions of the existence and nonexistence of the nonnegativeglobal Lp solutions and classical solutions, and discusses the asymptoticbehavior of solutions. The method used in this paper and obtained results arecompletly different from previous works ［1--4］, this paper not onlygeneralies the results of ［1--5］, but also improves the results of ［1］ on somerespect.