| In this paper,we study the initial boundary value problem for the generalized double dispersion equation.Firstly,the existence and uniqueness of the local solutions is obtained by the standard Fadeo-Galerkin method.Under the subcritical initial energy E(0)<d and the critical initial energy E(0)=d,we prove the global existence and blow up of the solutions by the potential well theory and the concavity method.The energy estimation of the global existence of the solutions is also given.The characterization of the potential well is the difficult part,and it is also one of the main tasks of this paper.Besides,the global existence and blow up of the solutions under the arbitrary positive initial energy are also given in the paper. |
