The Cauchy Problem For The Semilinear Beam Equation With Damped Term

We consider in the case that the initial data are small the Global existence to the Cauchy problem for the semilinear Beam equation with damped term in the weighted space L2.Firstly, we apply Duhamel principle and Fourier transform to its equivalent integral equation, Secondly, in L2-theory, we lead into weighted space, make up the the decay estimate, and additionally get existence of the solution to the linearized equation. Finally, using the contraction mapping principle, we give the existence to the cauchy problem of the nonlinear equation in the case that the initial data are small.