| In this thesis, we investigate the large time behavior of solutions for degenerate parabolic equation on the exterior domain, such as global existence in time and blow-up in a finite time, especially we are interested in the critical global existence curves and the critical Fujita curves. This thesis is divided into three chapters.In chapter 1, we introduce the known research related on our problems, and our main results.In chapter 2 and chapter 3. we discuss the boundary problems of Newtonian filtration equations and Non-Newtonian filtration equations on the exterior domain of the unit ball in RN, separately, i.e., (?)ui/(?)=Δuimi, x∈RN\B1(0),t>0, ▽uimi.v=ui+1qi(x,t), x∈(?)B1(0),t>0, ui(x,0)=u0,i(x), xzRN\B1(0) and (?)ui/(?)t=▽(|▽ui|pi-2▽ui_, x∈RN\B1(0),t>0, |▽ui|pi-2▽ui.v=ui+1qi(x,t), x∈(?)B1(0),t>0, ui(x,0)=u0,(x), x∈RN\B1(0), where mi>1, pi>2, qi> 0, i=1,2,...,n, N> 2,un+1=u1, B1(0) is the unit ball in RN with boundary (?)B1(0), v is the inward normal vector on (?)B1(0), and u0,i(x) are nonnegative, suitably smooth and bounded functions with compact supports that satisfy the appropriate compatibility conditions. Firstly we consider the radialized problem, then by constructing several kinds of upper and lower solution and the principle theorem, we obtain the large time behavior of solutions and also the global existence critical curves, Fujita critical curves. |
