Blow Up Criteria,Persistence Properties And Infinite Propagation Speed Of Solutions To The DGH Equation

In this thesis, we consider the Dullin-Gottwald-Holm equation. Firstly, we give a brief introductionabout Dullin-Gottwald-Holm equation, which includes some results obtained by other authors in this field. Subsequently, we list some results including Gronwall's inequality, Sobolev embedding theorem and the identity on (?), H_α~1 norm and we introduce some fundamental theorems on Dullin-Gottwald-Holm equation. At the same time, we rewrite the equation to get a proper form for our purpose. In the third part, we introduce the main results on blow up includes periodic case and nonperiodic case. Moreover we try to improve other results and get some new criterion on blow up. In Section 4 we discuss the persistence properties of the solution. Finally, we prove infinite propagation speed for the DGH equation.