一类非线性伪抛物系统的全局解与非全局解

Global existence and non-gloloal existence solutions with a nonlinear pseudo-parabolic system

该文研究了一类非线性伪抛物系统u_t-Δu-αΔut=v^p,v_t-Δv-αΔvt=w^q,w_t-Δw-αΔw_t=u^r的全局解与非全局解,其中p,q,r>1。首先建立了Fujita临界曲面pqr=(pqr)_c,即证明了当1<pqr≤(pqr)_c时,该方程的任意解都在有限时刻爆破;而当pqr>(pqr)_c时,方程既存在全局解又存在非全局解。而且根据初始值在无穷远处的衰减率,建立了第二临界曲面。

This paper deals with a class of nonlinear parabolic systems ut-Δu-αΔut=vp,vt-Δv-αΔvt=wq,wt-Δw-αΔwt=ur , subject to Cauchy boundary conditions, where p, q, r 〉 1. By establishing a curves of Fujitapqr = （pqr）c. It is proved that any solution blows up in finite time if 1 〈 pqr （pqr）c. while both global and non-global solutions coexist forpqr 〉 （pqr）c, And the second crit- ical curves is established accordin to the critical space-decay rate of initial data in infinity.