| In order to describe the motion and the invasion of tumor cells,many relate chemotaxis and haptotaxis models which consists of partial differential equations has been proposed and investigated by many researchers.This paper deals with the well-posedness problems,including the local existence,global existence,steady-state,the large time behavior,to a chemotaxis-haptotaxis model which include chemotaxis term and haptotaxis term.Since this model has a better understanding the interaction among tumor cells,tumor angiogenesis factors secreting by tumor cells themselves and the extracellular matrix,this means that tumor cells moves towards the tumor angiogenesis factors and move towards to the extracellular matrix,then the study of this model possess both theoretical and realistic significance.This paper divides into four chapters.In Chapter 1,we mainly introduce the background of chemotaxis and haptotaxis model,and introduce the research status of this models at home and abroad.Moreover,we will briefly summarize the main results in this paper.In Chapter 2,we consider the global boundedness of solutions to a parabolic-parabolic-ode chemotaxis-haptotaxis model.Given any smooth bounded convex domain in two dimensions and any smooth initial value,when the coefficient of diffusion function is suitable large in the sense that tumor cells diffuse fast,we prove that the system has a unique global bounded classical solution by improving the regularity and using the classical Moser iterative methods.In Chapter 3,we study the large time behavior of global bounded solutions to above chemotaxis-haptotaxis model.Firstly,we discuss the steady states of solutions to the system by some techniques.Secondly,based on some energy functions which decreases as time increases,the solutions will converge to above stationary solution as time tends to infinity.In Chapter 4,we summarize the main results in this paper and proposes some interesting problems to be done. |
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