Abstract :
We consider the nonlinear reaction-diffusion system
utyDusum1¨ n1 ,
¨tyD¨ sum2¨ n2 ,
subject to Dirichlet boundary conditions and m2)m1y1, n1)n2y1. We prove
that if m1F1, n2F1, and m2 n1F 1ym1. 1yn2 . all nonnegative solutions
are global, while if m1)1, or n2)1, or m2 n1) 1ym1. 1yn2 . both global
existence and finite time blow-up coexist.
