一类使局部化源抛物型方程组不同时爆破的临界指标

摘要

This paper deals with ut=△u+e^mu(x0,t)+pv(x0,t)=△v+e^qu(x0,t)+nv(x0,t) , subject to homogeneous Dirichlet boundary conditions, where x0 is any fixed point in a bounded domain of R^N. The complete classification on non-simultaneous and simultaneous blow-up is obtained by four sufficient and necessary conditions, h is interesting that, in some exponent region, large initial data u0 (v0) leads to the blow-up of u(v), and in some between, simultaneous blow-up occurs.%文章讨论一类具齐次Dirichlet边界条件的方程组ut=△u＋e^mu（x0,t）＋pv（x0,t）=△v＋e^qu（x0,t）＋nv（x0,t）．其中x0是R^N中有界区域内的固定点．通过四个充分与必要条件，得到解同时与不同时爆破的完整分类．有趣的是，在某指数范围内，大初值u0（V0）引起u（v）的爆破，而在这些初值之间，出现同时爆破．