Dynamics Analysis In Reaction-diffusion-advection Predator-prey System

The interaction pattern and distribution of species are of great significance in ecological protection and species survival,the more typical role is the predator-prey relationship,the existence and boundedness of solutions have been widely concerned.The stability,instability and other properties of corresponding solutions are also obtained.In this paper,we study a Lotka-Volterra type predator-prey model in one-dimensional advective homogeneous environment.By using upper and lower solutions and prior estimates,we study the local existence and properties of semi-trivial steady-state solutions.The global existence and boundedness of solutions are analyzed by constructing invariant region.The stability/unstability of the semi-trivial steady state solution is analyzed by the linearization principle.Finally,the persistence result of the coexistence solution is obtained by the existence of the global attractor.