The Global Solutions For A Kind Of The Nonlinear Beam Equation With Strongly Damping And A Memory

Nonlinear beam equations with a memory term are vital problems in mathematical field in recent years. Especially, those form viscoelastic mechanics with a memory term are focused on by researchers. In this thesis, we investigate the results that the existence and uniqueness of the global solutions of the following initial-boundary value problem for the nonlinear viscoelastic beam equation with a memory term, when they satisfy strongly damping. under the certain the initial conditions u(x,G)=u0(x) u(x,0)=u1(x) and subject to the boundary conditions u(0,0=u(l,t)=H(2)(0,t)=u(2)(l,t)=0The particular content is following:First, we made simple sum-up and comment on the developing and actuality of study on partial differential equations relevant.Secondly, this article will give some important lemmas, and the part of the symbols is explained.Thirdly, we will prove the existence and uniqueness of weak solutions by Faedo-Galerkin method.At last, we will prove the existence and uniqueness of strong solutions.