Qualitative Analysis To The Degenerate And Singular Reaction-Diffusion Equations

In this thesis,we study the properties of solutions to three kinds of nonlinear reaction-diffusion models based on the compare theory and the methods of the super and sub solutions, which belongs to basic theory of the reaction-diffusion equations.The thesis includes four parts.In part one, we briefly introduce the basic conceptions and conclusions of the reaction-diffusion models and the basic knowledge of Bessel function. We also give a briefly introduction to the background and development of the reaction-diffusion equations.In part two, we discuss the properties of global existence and blow-up of solutions to a kind of the problem of the double degenerate reaction-diffusion system with non-local source. Firstly, we prove the existence of the classical solution to the regularizing problem, then, give the existence of the local classical solution of problem. Secondly, using the method of the super- and sub- solutions and compare theory, we get the conditions for the global existence and blow-up of the solutions by constructing the various super and sub solutions.In part three, we discuss a class of singular and degenerate reaction-diffusion equations with weakly coupling term. We obtain the sufficient conditions that the solution of the problem exists globally and blows-up in finite time respectively by using the super- and sub-solution techniques.In part four, we investigate a class of singular and degenerate nonlinear parabolic equation with nonlocal source and absorption terms. The conditions that solution exists globally and blows up in a finite time are given by introducing the upper and lower solutions.