A Class Of Reaction Diffusion Absorption Of The Critical Indicators Of The Equations

This paper mainly deals with critical exponents for a parabolic system with inner absorption and coupled nonlinear boundary flux. A detail analysis is given to the interactions among the multi-nonlinearities in the system. The critical exponent of the system is simply described via a characteristic matrix equation introduced.In the introduction, we give backgrounds and applications of reaction-diffusion equations. The second chapter contains some preliminaries related to this paper, as well as some of current situations in the field. The main part of this paper is chapter 3, where we study a class of reaction-diffusion system with muliti-nonlinearites, i.e., nonlinear reaction (absorption) and nonlinear boundary flux. The critical exponents and the character of solutions are determined. These results are simply described via a characteristic matrix equation introduced to show the interactions among all the non-linearites. Finally, in the last chapter, we discuss the blow-up rate of solutions to this problem.