Global existence and nonexistence for some degenerate and quasilinear parabolic systems

The author discusses the degenerate and quasilinear parabolic systemut=uαvβΔu+aupvqandvt=uθvηΔv+burvs, with Dirichlet boundary conditions in a bounded domain Ω   and shows that the global existence depends crucially on the sign of the difference (q−β)(r−θ)−(α+1−p)(η+1−s)(q−β)(r−θ)−(α+1−p)(η+1−s) and the domain Ω.