Note On The Properties Of Solutions For A Class Of Nonlinear Reaction-diffusion System

By the method of upper and lower solutions, in this paper, we deal with a kind of quasilinear equations and equations with nonlocal sources. We obtain some sufficient conditions of global existence and finite time blow up for the solutions . The main content of this paper is divided into three chapters: In chapter two, we discuss the following degenerate parabolic system:with initial value conditions:and boundary conditionswhere is bounded domain in R^N with smooth boundary are nonnegative functions in .Under the conditions of we obtain three main theorems on global existence and finite time blow up of the solutions ,and at the same time we think about the effect of and the shape ofthe domain on existence of solutions.In chapter three, we discuss the critical value We give fourtheorems on global existence and finite time blow up of the solutions.In chapter four, we discuss the following degenerate parabolic system with nonlocal source:where is bounded domain in R^N with smooth boundary are nonnegative functions in .We also give two theorems on the global existence and finite blow up of the solutions about (4)-(6).In chapter five ,we discuss the case of (l)-(3) when p_i=0 (i= 1,2,3), and thesystem is made up of two equations:where From a new angle ,we investigate the effect of behavior of initial date u₀(x),v₀(x) at infinity on the non-global existence of weak solutionsto (5.1)-(5.2).