Global Behavior Of Sulutions For A Predator-Prey Cross-diffusion Model With Disease In The Prey

Global behavior of solutions is considered for a cross-diffusion SIP modelwhereΩis a bounded domain in Rⁿ with smooth boundary (?)Ω,ηis the outward unit normal vector on (?)Ω, u₁,u₂,u₃ are the densities of susceptible prey, infected prey and predator respectively. This paper is divided into three chapters.In Section 1, the stability of nonnegative equilibrium points and the uniform boundedness of global solutions for the model (1) of ODE type are discussed.In Section 2, the weakly coupled reaction-diffusion system (1) (i.e.α_ij = 0(i,j = 1, 2, 3))is discussed. The stability of nonnegative equilibrium points and the uniform boundedness of global solutions of problem (1) are given and the stability of nonnegative equilibrium points is discussed by linearization and Lyapunov methods.In Section 3, using the method of energy estimates and Gagliardo-Nirenberg type inequalities, the existence and uniform boundedness of nonnegative global solutions for model (1) are established when the space dimension is one. Moreover, the stability of desease free equilibrium points are proved by Lyapunov method.