A Degenerate Parabolic System Of A Degenerate Diffusion Equation The Existence Of The Bursting

This thesis is devoted to the existence and blow-up for the positive solution of degenerate parabolic system and a class of nonlinear degenerate diffusion equation with nonlocal source .The thesis consists of three parts: In chapter 1 , the basic background advanced studies some method and preliminaries are introduced.In chapter 2,1 consider a class of nonlinear degenerate parabolic system: Where Ω is a bounded domain in R ^N (N > 1) with smooth boundary, 1 < r < 2, u₀ (x) v₀ (x) are the nonnegative differentiable C functions. With the compatibility condition ,we haveuo (x) = v₀ (x) = 0 on Ω. I apply regularized method to construct an appropriate function ofthe solution ,then seek its upper and lower bound,at last, I prove the local existence and blow-up of the solution by sub-supsolution.In chapter 3 ,1 consider a class of nonlinear degenerate diffusion equation with nonlocal source:Where is smooth ,r > 1, u0(x) .I consider an ordinarydifferential problem , then find its bounded positive solution as the appropriate function's upper bound, use the same method to prove the solution's global existence and blow-up.