Global Existence And Blow-up Analysis For A Multi-coupled Parabolic System

This paper deals with a heat equation with nonlinear source and nonlinear boundary flux, especially containing absorption on the boundary. A characteristic algebraic equation system covering the all six nonlinear exponents of the system is introduced to get a simple description for the critical exponent of the system.In the introduction, we give the background to the study of nonlinear parabolic equations. In Chapter 2, we introduce the basic knowledge on them which will be used here without proving. In chapter 3, we give a simple depiction for the main problem and results studied in this paper. We will introduced the so called characteristic algebraic system related to the problem and get simple descriptions for the blow-up criteria. In Chapter 4, by using the method of super and sub-solutions, we get the critical exponent to determine the global and non-global solutions.