Persisitence Properties Of Strong Solutions Of Some Nonlinear Partial Differential Equations

Nonlinear partial differential equation is a long history of discipline, which appears as a significant mathematical model in various fields, its solution method and solution prop-erties are mainly studied. In this thesis, our work is to research the persistence properties of the Camassa-Holm-Novikov equation, a generalized Novikov equation and two component Novikov equations. Among them, the Camassa-Holm-Novikov equation is seen as a combina-tion of Camassa-Holm equation and Novikov equation, while the generalized Novikov equation is a combination of Camassa-Holm equation, Degasperis-Procesi equation and Novikov equa-tion. It is shown that the strong solutions of the three equations also must decay exponentially at a later time when the initial data together with its derivatives decay exponentially.We now finish the abstract by outlining the rest of the thesis.Chapter 1 is a preliminary chapter, which includes the history of soliton theory and the background of the related integrable systems(i.e. Camassa-Holm equation, Degaperis-Procesi equation and Novikov equation), states certain related knowledge and shows the main results of this thesis.In Chapter 2, the Camassa-Holm-Novikov equation is introduced firstly, and then the conclusion of the persistence properties for this equation is turned out, and detailed proof process is presented at last.In Chapter 3, it presents a generalized Novikov equation and its persistence properties, and it is worth mentioning that the proved method is slightly improved from chapter 1.In Chapter 4, considered herein is the two component Novikov equation, whose formu-lation is quite different from the first two equations, we use the same method to obtain its persistence properties, which is a promotion of the method above in a sense.In Chapter 5, the thesis is summarized and the follow-up work is forecasted.