Uniform Boundness And Convergence Of Global Solutions To The Reaction-diffusion System

In this paper, We study nonlinear parabolic system, then the existence of local solutions and global solutions with their unifom boundness and convergence are obtained. This paper is composed of three chapters, and in chapter 1 we present introduction, some basic knowledge. In chapter 2 and chapter 3, we consider some related problems about the solutions to the following system (P): under these three conditions:Smooth global solutions were obtained in [5-10], which investigated system with only two spieces mutual competing. While Martinez[13] considered thefollowing Lotka-Volterra diffusion system(Po) with three spieces mutual competing, and the effect of diffusion in the existence of non-constant steady states were studied.Strongly-coupled parabolic system(P) in this paper is that a third spieces is added to the system in[5-10].By using the abstract parabolic equations in Hilbert space, we obtain theexistence of local solutions. Then we estimate the boundness of H1-norm to the solutions under conditions, which independ on time. At the same time we obtain the boundness of H-norm to the solutions under conditions whenThus we establish global solutions to (P) and their uniformboundness under conditions, finally we prove the convergence under conditions with some more certain conditions.