Extinction Of Solutions To Nonlinear Fast Diffusion Equations With Nonlinear Sources

In this thesis,we investigate the extinction phenomenon of the fast Newtonian filtration equations with nonlinear sources and the fast Non-Newtonian filtration equations with nonlinear sources.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,we study the extinction phenomenon of the fast Newtonian filtration equations with nonlinear sources,namely:where ? be a bounded domain in RN(N>2),with smooth boundary(?)?,0<mi<1 and Pi>0(i = 1,2,...,n),ui0(x)are nonnegative L00 functions.This problem can be used to describe the phenomenon of diffusion exist in nature widely,in which 0<mi<1,it corresponds to the fast diffusion case,the solution can be extinguished at a finite time.We say that the solution(u1,u2,...,un)has a finite extinction time T if T>0 is the smallest number such that each ui(x,t)(?) 0 for almost every ?×(T,?).When the problem is used to describe the combustion of the combustible mixture and the proliferation of biological species,extinction means the cessation of the material combustion or the extinction of the species.In chapter 3,we study the extinction phenomenon of the fast Non-Newtonian filtration equa-tions with nonlinear sources,namely:where ? is a bounded domain in RN(N?1)with smooth boundary(?)?:1<?i<2,?i>0,and the initial data ui0,ui0?L?(?)?W01,?i(?),i=l,2v..,n.This problem can be used to describe t he phenomenon of diffusion exist in nature widely,in which 1<?i<2,it corresponds to the fast diffusion case,the solution can be extinguished at a limited timeWe give the sufficient conditions of the existence of extinction solutions to the above two problems in chapter 2 and chapter 3,respectively.