中文摘要：

研究具有非局部边界和非局部源项的一类抛物型方程组非负解的整体存在与爆破性.用上下解方法得到了方程组解的临界指数p=（p1＋q1）…（pk＋qk）-1,证明了：当p≤0,且0≤∫Ωψi（x,y）dy〈1时,方程组存在整体解;当p〉0时,对于充分大的初值,方程组的解在有限时刻爆破.并讨论了解的爆破率.结果表明,初值和指数的大小对方程组的解有较大影响.

英文摘要：

The authors investigated the global existence and blow-up properties of nonnegative solutions for a class of nonlocal parabolic systems with nonlocal boundary conditions. With the help of the super- and sub-solution methods, the critical exponent of system was gained. And it＇s proved that if p= （P1＋q1）（Pk＋qk）- 140 and 0 whereas if p〉0, then the solution Moveover, the exact rate of the blow and exponents play an important role （x,y）dy 〈 1, every nonnegative solution is global, blows-up in finite time if the initial data is sufficiently large. -up is obtained. The results show that the size of initial values in the properties of the solutions.