The initial-boundary value problem for the generalized double dispersion equation

We consider the initial-boundary value problem for the generalized double dispersion equation in all space dimension. Under the suitable assumptions on the initial data and the parameters in the equation, we establish several results concerning local existence, global existence, uniqueness, and finite time blowup property. The exponential decay rate of the energy is proved for global solutions. The sufficient and necessary conditions of global solutions and finite time blowup of solutions are given, respectively.