变分流方程组初边值问题的Blow-up性质

ON THE BLOW-UP OF SOLUTIONS OF INITIAL BOUNDARY VALUE PROBLEM FOR VARIATIONAL FLOW SYSTEM

§1 引言及主要结果设 Q 是 Rn 中具有光滑边界（?）Ω的有界区域,考虑抛物变分流方程组（（?）ui）/（（?）t）=sum from α=1 to n （?）/（（?）Xα） F?（x,u,Du）-Fui（x,u,Du） （1）（（x,t）∈Ω×[0,T）,i=1,2,…,N)的第一初边值问题（?

In this paper,we considered the following parabolic variational flow syst-em(?)Under suitable conditions on F and g,we proved that the solutions Blow—upin a finite time provided the initial energy is negtive.Similar results wereproved for the first IBVP and for the system of hyperbolic type.