Periodic boundary value problem and cauchy problem of the generalized cubic double dispersion equation

In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation utt  - uxx - auxxtt + bux4 - duxxt = f(u)xxutt  - uxx - auxxtt + bux4 - duxxt = f(u)xx are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.