Qualitative Analysis Of Two Types Of Models With Hyperbolic Partial Differential Equations

This paper studies two types of hyperbolic partial differential equation models,one is the King-Ward tumor model,and the other is the shallow water wave equation.The specific article structure is as follows:The first chapter of this paper is introduction,including the research background,research significance and research status of this topic.The second chapter of this paper studies a King-Ward tumor model.For this model,by applying the method of characteristic curves and the Banach fixed point theorem,the existence and uniqueness of the global solution of the model are proven.Finally,it is proven that wlile KR=0,the radius of the tumor tends to infinity over time,i.e.(?)For hyperbolic partial differential equations combined with Robin boundary condition,no article has been studied before.So,this paper provides some methods for the follow-up research on such problems..The third chapter of this paper studies a kind of shallow water wave equations.For the shallow water wave equations,we mainly use the method of characteristic curves to study the Cauchy problem of the B-family equations involving two-component with the initial data(u0,?0-1)?(H1(R)?W1,?(R))×(L2(R)? L?(R)).