Stability Of Two Types Of Competitive Reaction-diffusion-convection Model Solutions

With the development of bio-mathematics,the study on species competition in advective environment has become an important research topic for domestic and foreign scholars.Nowadays,a large number of mathematical models have been proposed for this kind of problems.In particular,the competitive reaction-diffusion-advection models have become an important research direction in this field.Here we study the following two kinds of competitive reaction-diffusion-advection models:(?) and (?)In this thesis,we study the stability of the solutions of two kinds of compet-itive reaction-diffusion-advection models by using the knowledge of the maximum principle,the eigenvalue theory and the monotone dynamical system theory.The main contents are organized as follows:In the second chapter,we mainly study a reaction diffusion model with No-flux/Hostile boundary conditions.Firstly,we apply the maximum principle and the eigenvalue theory to establish the existence and uniqueness of the single species model.Secondly,the asymptotic behavior of the solution is discussed by using the method of upper and lower solutions.Thirdly,the existence and the stability of semi trivial solutions of the two species model are studied by the linear stability theory.Finally,by the monotone dynamical system theory,we investigate the longtime behavior of the system.In the third chapter,we mainly study a reaction diffusion model in a water column.Firstly,the existence and stability of positive solutions of single species are obtained by using the maximum principle and eigenvalue theory.Secondly,the existence and the stability of semi trivial solutions of the two species model are studied by the linear stability theory.Finally,the influence of each parameter on the stability of the solution is studied.