非线性耦合的非局部扩散系统的临界曲面

The Critical Curved Surface for Nonlinear Coupled Nonlocal Diffusion System

研究了一类非线性耦合的非局部扩散系统ut=J*u-u+vp,vt=J*v-v+wq,wt=J*w-w+ur的柯西问题。首先根据是否存在全局解建立了Fujita曲面1<pqr≤(pqr)_c。即证明了:如果1<pqr≤(pqr)_c,其任意正解都在有限时刻爆破;而当pqr>(pqr)c时,则既存在全局解也存在非全局解。然后根据初始值在无穷远处的衰减率建立了第二临界曲面。

Abstract： This paper discusses about the Cauchy problem tbr a nonlinear coupled nonlocal diithsion system ut = J＊u -u ＋vp,vt = J＊v-v＋wq,wt = J＊w-w ＋u. Firstly,it is proved that the Fujitacurved surface is （pqr）c = 1 ＋ 2/Nmax{pq ＋p ＋ 1 ,qr ＋ q ＋ 1 ,pr ＋ r ＋ 1} based on whether there exists global solutions. Namely,if 1 〈 pqr 〈_ （pqr）c ,then every nonnegative solution blows up in finite time, but torpqr 〉 （pqr）~ , there exists both global and non-global solutions to the problem. Then, the secondal7 critical curved surface on the space-decay of initial value at infinity is established.