The Well-posedness And Existence Of Global Attractor For Tumor Growth Model

In this thesis,the interface model of tumor growth and diffusion under Neumann homogeneous boundary conditions is studied.The model is involved in Cahn-Hilliard equation coupled with a reaction-diffusion equation.Cahn-Hilliard equation is mainly used to describe the tumor phase field,while the reaction-diffusion equation is used to describe the influence of the change of nutrient concentration on the tumor phase field.In this thesis,the well-posedness of the solution of the tumor growth diffusion interface model is proved by deriving some priori estimations,combining with Aubin-Lions compactness lemma and Lebesgue's dominated convergence theorem.It is proved that under the appropriate assumptions on model parameters,the corresponding initial boundary value problem generates a dissipative dynamic system,which has a global attractor in the appropriate phase space.