一类使局部化源抛物型方程组不同时爆破的临界指标

Critical Exponents for Non-simultaneous Blow-up in a Localized Parabolic System

文章讨论一类具齐次Dirichlet边界条件的方程组ut=Δu+emu(x0,t)+pv(x0,t),vt=Δv+equ(x0,t)+nv(x0,t).其中x0是RN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.

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.