Global Dynamics Study Of Diffusion-Convective Competitive Systems Over A One-Dimensional Domain

In this thesis,we mainly investigate a competitive reaction-diffusion-advection system arising in river ecology.Under certain conditions,the a priori estimate regarding the linear stability(non-degeneracy)of any coexistence steady state is given.Then by the theory of monotone dynamical systems,a complete classification on all possible long time dynamical behaviors is obtained.Furthermore,by choosing the competition coefficients as bifurcation parameters,the global dynamics is further determined.The main body of this thesis is divided into three chapters.In the first chapter,a brief introduction on the biological background and recent advances is exhibited.Moreover,the problem we are mainly interested in and the main conclusions we obtained are displayed.The second chapter,as a preliminary,mainly contains some fundamental results including the celebrated Krein-Rutman theorem and the monotone theory.The third chapter is primarily devoted to the main proofs.Precisely,in subsection 3.1,under certain mild conditions,all possible coexistence steady states are proved to be linearly stable and also,the phenomenon that the two semi-trivial steady states are stable simultaneously cannot occur;in subsection 3.2,combining the results in the previous subsection with the theory of monotone dynamical systems as well as the upper and lower solution method,the long time dynamical behaviors are completely classified;in subsection 3.3,by the virtue of the theory of principal eigenvalues,a picture on the global dynamics is shown in the plane of bifurcation parameters.