The Study Of A Three-species Predator-prey Model With Prey-taxis And Competition

In this thesis,we concern with the following three-species predator-prey model with prey-taxis and competition:in a bounded domain Ω(?)R2 with smooth boundary,where all parameters d1,d2,d3,χ1,χ2,χ3,r1,r2,r3 和 a,b1,b2 are positive constants.Utilizing coupling energy estimates and semigroup theory,we establish the global boundedness of classical solutions for σ>5/3 and appropriate initial data.In addition,by constructing Lyapunov functional,the steady state of the three-species coexistence constant is asymptotically stable under appropriate conditions.The thesis is organized as follows:In Section 1,we mainly introduce some background and research process as well as our main results.It will be devoted to giving some statement of a priori bounds of solutions in Section 2,we will give some results including the local existence theorem and some basic estimates of system which are used for our further proof frequently.In Section 3,we apply Lp theory to obtain the maximum estimate for original population u.Then hard work is carried out in Section 4,where we derive joint estimates including‖▽u(·,t)‖L4,‖Δv(·,t)‖L2 and ‖w(·,t)‖L2 by elaborate analysis.Finally,together with the previous conclusions,we end our proofs in Section 5.