Global and blowup solutions for general quasilinear parabolic systems

This paper deals with global and blowup solutions of the general quasilinear parabolic system ut=α(u,v)Δu+f(u,v,Du)ut=α(u,v)Δu+f(u,v,Du) and vt=β(u,v)Δv+g(u,v,Dv)vt=β(u,v)Δv+g(u,v,Dv) with homogeneous Dirichlet boundary conditions. We will give sufficient conditions such that the solutions either exist globally or blow up in a finite time. In special cases, a necessary and sufficient condition for the global existence is given. We also discuss a degenerate case.