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中文摘要：
利用Galerkin方法,研究一个具有非线性边界条件的梁的振动方程模型,utt＋uxxxx-∫t0k（t-τ）uxxxxdτ-M（∫L0｜ux｜2dx）uxx=0在[0,L]×R＋,这个梁的振动模型具有固定端x=0和非线性支撑端x=L,通过在x=L处添加阻尼结构来研究该方程的整体解.
英文摘要：
In this paper,we consider a equation utt＋uxxxx-∫t0k（t-τ）uxxxxdτ-M（∫L0｜ux｜2dx）uxx=0在[0,L]×R＋under non-linear boundary conditions which model the vibrations of a beam clamped at sc ~--- 0 and supported by a non-linear bearing at a： = L. By adding only one damping mechanism at x = L, we prove the existence of a global solution.
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