摘要
In this paper, we study the higher-order semilinear parabolic system{ut＋（-△）^mu=a｜v｜^p-1v,（t,x）∈R^1＋×R^N,vt＋（-△）^mv=b｜u｜^q-1u,（t,x）∈R^1＋×R^N,u（0,x）=φ（x）,v（0,x）=ψ（x）,x∈R^N, where m, p,q 〉 1, a,b ∈R. We prove that the global existence of mild solutions for small initial data with respect to certain norms. Some of these solutions are proved to be asymptotically self-similar.
基金
This work was supported by the National Natural Science Foundation of China 10701024 and the Natural Science Foundation of Tianjin of China （08JYBJC12100）.
