弹性矩形板方程在非线性边界条件下整体解的存在唯一性

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w⁰∈W，w¹∈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w⁰∈W₁，w¹∈W₁的条件关键词：弹性矩形板方程非线性边界条件初边值问题整体解

The existence and uniqueness of the global solution for the viscoelastic-plate equation under nonlinear boundary conditions

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 w⁰∈W，and w¹∈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 w⁰∈W，and w¹∈W₁，the existence and uniqueness of a global weak solution w(t) is also proved by using Galerkin method.