The Asymptotic Behavior Of The Solution Of A Chemotaxis-haptotaxis Model

This dissertation deals with the asymptotic behavior for the following chemotaxis-haptotaxis model (?) where Ω(?)Rn is a bounded smooth domain,χ,ξ,μ>0,τ∈{0,1},and the diffuse function satisfies D(u)≥c0(u+1)m,-1,where m>2-2/n,c0>0,u>0.The main contents of this dissertation are as follows:In Chapter 1,we mainly introduce the actual background and the research status,and state the main research content.In Chapter 2,we mainly study the asymptotic behavior for the higher-dimensional parabolic-parabolic-ODE chemotaxis-haptotaxis model.Assume that (?) we derive the solution of model satisfies(u,v,w)→(1,1,0)as the time t→∞,moreover,the rate at which the model’s solution converges to a stable solution decays exponentially.In Chapter 3,we mainly study the asymptotic behavior for the higher-dimensional parabolic-elliptic-ODE chemotaxis-haptotaxis model.Assume that (?) the component u of the model’s solution convergence to the steady state 1 in the norm Lp {Ω)(p≥2)as the time t→∞,and the component v of the solution of this model convergence to the steady state 1 in the norm U∞(Ω)as the time t→∞,moreover,the rate at which of the components u,v of the model’s solution decays exponentially.In Chapter 4,we summarize the main results in this dissertation and make corresponding expectations.