Global Existence Of Solutions For A Class Of Chemotaxis-haptotaxis Model With MDE Concentration

We consider the following the cancer invasion model(?),in a bounded smooth domain ?(?)R2 with zero-flux boundary conditions,where x,?.? and? are positive parameters.In this thesis,the equation is a chemotaxis-haptotaxis model to describes the interactions between cancer cells,matrix degrading enzymes and host tissues during cancer cell invasion.? reflects the self-reconstruction process of extracellular matrix.The purpose of this thesis is to establish the existence of the solution to the initial boundary value problem of the above model.First,the local existence of the solution is obtained with the help of the fixed point argument.Then using Young inequality,Cauchy-Schwarz inequality,Lp estimates and the Lq-Lp estimates for the heat semigroup,the solution of the prior estimates is changed from L1(?)to Lk(?),k>2.Finally,based on the Alikakos-Moser iterative technique,it is proved that the problem has a unique global classical solution.