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

Abstract

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.