Global Existence Of Solutions For The Initial Value Problem Of The Kawahara Equation

This dissertation consists three chapters.In Chapter 1,by using the method of the k-multipler and the k-linear functional,we obtain a sequence of almost conserved qualities and the sublinear estimates in the Bourgain's space for the following initial value problem to the Kawahara equationFurthermore,by combining with the local well-posedness results gotten in[13],we establish the global existence of the solutions of the initial value problem to the Kawahara equation with the small data in H~s for s＞-1.In Chapter 2,we consider the following Cauchy problem of the non-homogeneous Kawahara-type equations with the interaction of dissipation and dispersionwhereαis dissipative coefficient andβis dispersion coefficient.We obtain the stability, uniqueness and blow-up for the solutions of the above Cauchy problem.In Chapter 3,we study the following Cauchy problem of the Kawahara-Buegers equationwhereα＞0 is dissipative coefficient andβ＞0 is dispersion coefficient,x∈R.The uniqueness and stability are established for the solutions of the Cauchy problem to the Kawahara-Buegers equation.Furthermore,the decay characteristics of the solutions are also obtained as t→∞.