具有记忆项的基尔霍夫型梁方程在非线性边界条件下的整体解

Global Solution in Non-linear Boundary Conditions for Kirchhoff-beam Equation with Memory Term

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.

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.