With The Trend Of Movement Of The Reaction Diffusion Equation

We consider reaction-diffusion-advection model of two populations that have a tendency to disperse up the gradient of fitness.This paper includes three chapters. Now we will describe them briefly one by one.In chapter 1, we recall the history and introduce the backgrounds of the research on the reaction-diffusion-advection equations and the main work of this thesis.In chapter 2, we study a competing species model of two organisms. The two species move up along the gradient of▽(lnm). The diffusion coefficients of the two species are differ-ent. We consider the effect of the different diffusion coefficients for the results of competing species.In chapter 3, we discuss a competing species model of two species that use the different disperse strategies. One of the species move up along the gradients of▽(m-u-v) while the other species move up along the gradients of▽(lnm). We consider the existence of the coexistence state.