Persistence Properties And Analyticity For A New Two-Component Generalized Camassa-Holm System

In this thesis,we study the persistence properties,optimal decaying estimates and analyticity of solutions to the initial value problem for a new generalized two-component Camassa-Holm-type system.The persistence properties imply that the solutions of the equations decay at infinity when the initial data satisfies the condition of decaying at infinity.And the analyticity in this paper means that solutions of Camassa-Holm-type system above are analytic in both variables,globally in space and locally in time.The method of estimate with weight function is a classical one to study persistence properties and.Generalized Ovsyannikov theorem is a new method to discuss the analyticity of the solutions for the Camassa-Holm-type system and is weaker than the classical Cauchy-Kovalevsky theorem.On the basis of the local well-posedness results,we prove the persistence properties by using weight function estimation method and the analyticity by using Generalized Ovsyannikov theorem of the strong solution for the Camassa-Holm-type system above.The main contents of this thesis are as follows:Chapter one,we introduce the purpose and significance of the persistence properties and analyticity and the background,progress of the Camassa-Holmtype system above;Chapter two,we describe concretely the related definition,preliminary theories and the symbols required to solve the problem;Chapter three,by using weight function estimation method,we obtain the persistence properties of the Camassa-Holm-type system above;Chapter four,we apply Generalized Ovsyannikov theorem to prove the analyticity of the Camassa-Holm-type system above.