Smoothness of the Global Weak Solutions for a Kind of Nonlinear Fourth Order Wave Equations

The initial boundary value problem of a kind of nonlinear fourth-order wave equations describing beam vibrations was studied. With Galerkin method, it is proved that the smoothness of the global weak solution can be improved if the smoothness of the initial value is improved. By virtue of Sobolev s embedding theorem, the global weak solutions become classic ones when the initial value is appropriately smooth.