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 ?(?)Rn is a bounded smooth domain,?,?,?>0,??{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 {?)(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?(?)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.