【摘要】 研究一类描述梁振动的非线性四阶波动方程的初边值问题.用Galerkin方法证明了整体弱解的光滑性随初值的光滑性提高而提高.由Sobolev嵌入定理可知,当初值的光滑性适当高时,弱解成为经典解.更多还原

【Abstract】 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.更多还原