中文摘要：

考虑了在非线性边界条件下的弹性矩形板方程.利用Galerkin方法,首先证明了该方程在非线性边界（a）及初值w^0∈W,w^1∈W的条件下初边值问题存在唯一整体弱解w（t）.其次证明了该方程在非线性边界（b）及初值w^0∈W^1,w^1∈W^1的条件下初边值问题也存在唯一整体弱解w（t）.

英文摘要：

In this paper,we consider the viscoelastic-plate equation under non-linear boundary conditions.Firstly,by the aid of Galerkin method,under non-linear boundary conditions（a） and the initial values w^0∈W,and w^1∈W,we prove the existence and uniqueness of a global weak solution w（t） for the initial boundary value problems.Secondly,under non-linear boundary conditions（b） and the initial values w^0∈W,and w^1∈W1,the existence and uniqueness of a global weak solution w（t） is also proved by using Galerkin method.