Qualitative Analysis Of A Mathematical Model For Tumor Growth With Necrotic Core And A Shallow Water Wave Model

In this paper,we study a mathematical model of tumor growth with necrotic core and a shallow water wave model.We obtain qualitative analysis of the corresponding problems by strict mathematical analysis.In chapter 1,we give an introduction to the research background and its current development of the mathematical model of tumor growth with necrotic core and the shallow water wave model.In chapter 2,we study a mathematical model of necrotic core tumor growth with Robin’s free boundary.We prove the existence uniqueness of the stationary solution of the model and the asymptotic behavior of the solution by strict mathematical analysis.During the research process of this chapter,we improve the method,which provides a little idea for the follow-up study of such problems.In chapter 3,we study the solution of the generalized Camassa-Holm equation,which is mainly considering the weak well-posedness of solution for initial value u₀ in space H¹H¹∩W^1,∞（（?））.We use the method of characteristics to investigate the existe-nce and uniqueness of the local solution,and giving the conclusion of the weak continuous of the weak continuous dependence on initial data for the equation.