Properties Of Soultions Of Two Kinds Of Shallow Water Equations

In this thesis,the properties for solutions of two kinds of shallow water equations are focused.To begin with,the research background will be introduced briefly on the Holm-Staley b-family equations and a kind of the fifth order Camassa-Holm model,referred to as FOCH model.At the same time,the basic definitions and lemmas are also given in this section.Then,the Holm-Staley b-family equations with weak dissipation terms are investigat-ed.It is showed that if the initial datum u₀?x? has a compact support,the corresponding solution u?x,t? does not have a compact-support any longer in its lifespan,verifying the propagation speed infinite.Besides,with the existence of global solution,we obtain the large time behavior of the support of momentum density with the initial data compact supported.Finally,the properties on the fifth order Camassa-Holm model of the solutions are explored in this section.the blow-up criteria of the solution of this model in a limited time and the global existence under different conditions are given.Then,we discuss the infinite propagation velocity of the solution and obtain the large time behavior of momentum density support under the condition that the initial value have a compact support set.