The behaviour of the solution of the initial-boundary value problem \(U_ t+\gamma D^ 4U=D^ 2\Phi (u),\Phi (u)=\gamma_ 2u^ 3+\gamma_ 1u^ 2+\gamma_ 0u,\) \(D=\partial /\partial x\), \(\gamma,\gamma_ i\) are constants, \(Du=\gamma D^ 3u-D\Phi (u)\) \((x=0\), \(x=L)\) \(u(x,0)=u_ 0(x)\) is studied using a finite element Galerkin method. Also, numerical experiments are discussed.