Global Existence And Nonexistence For Some Degenerate And Quasilinear Parabolic Systerm With Convection

The author discusses the degenerate and quasilinear parabolic systemwith convection and Dirichlet boundary conditions in a bounded domainΩand shows that the global existence and nonexistence depend crucially on the sign of the differcence pq-(α+1)(β+ 1),the domainΩand the convection term.We obtain the global existence for any smooth initial values when pq-(α+1)(β+1)＜0 and proof that the global solutioins do not exist for some large initical values when pq-(α+1)(β+1)＞0.In critical case pq-(α+1)(β+1)=0,the size of the domain and convection term paly a significant role in the existence or nonexistence of global solutions.In this paper,we estimate the integral of a ratio of one solution to the other, rather than construct a pair of super-sub solutions ,to obtain lower and upper bounds for the solution of (3.1.1).This method shows successful in proving existence and blowup problems.