Finite time Blow up of solution of Cauchy problem for the multidimensional generalized double dispersion equations with arbitrary initial energy

In this paper, we consider the Cauchy problem for the multidimensional generalized double dispersion equations. We prove that, for certain initial data in the unstable set, the solution with arbitrarily positive initial energy blow up in finite time. This result improves earlier ones obtained by Xu and Liu [R. Xu and Y. Liu, Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations, Journal of Mathematical Analysis and Applications vol. 359, pp. 739-751, 2009.] in which the blow up result is considered under E(0) <; d.