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 w(0) is an element of W, and w(1) is an element of 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) is an element of W, and w(1) is an element of W-1, the existence and uniqueness of a global weak solution w(t) is also proved by using Galerkin method.