Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations

We study the Cauchy problem of a class of multidimensional generalized double dispersion equations utt−Δu−Δu−tt+Δ2u+kΔut=Δf(u)utt−Δu−Δu−tt+Δ2u+kΔut=Δf(u). We prove the global existence of weak solution under some assumptions on the nonlinear term and the initial data.