The Global Existence And The Finite Time Blow Up Of Solution To Degenerate Parabolic Systems

This thesis deals with the global existence and the finite time blow-up of solutions to de- generate parabolic systems coupled via nonlinear sources or (and) nonlinear boundary flux of exponential types. We prove the local existence of the solution to systems by using regularization skill, and obtain the sufficient condition of the global existence and the finite time blow-up of solution to systems by using upper-lower solution method.We give the background of the problem that we consider and the history to the study of nonlinear parabolic equation in the introduction. In Chapter 2, we introduce the basic knowledge on them that will be used here without proving.In Chapter 3, we deal with following initial value and boundary value problem of degenerate parabolic systems First of all, the local existence of solution is proved by using regularization skill; and then, using upper-lower solution method, we obtain the sufficient conditions of the global existence and the finite time blow-up of the solusion, they are respectively:In Chapter 4, we study following initial value and boundary value problem of degenerate parabolic systems coupled via three variables of exponential types We use the same method as In Chapter 3, first of all, the local existence of solution to be proved. Then, we obtain the sufficient condition of solution for the finite time blow-up is m≥2, In Chapter 5, we study following initial value and boundary value problemUsing upper-lower solution method, we obtain the sufficient conditions for the global existence and the finite time blow-up, they are respectively:...