Kirchhoff方程有限维摄动解的分析

对于描述两端固定的张紧着的弦的横振动的Kirchhoff方程的初边值问题,当初始位移和速度均为有限正弦级数时,用多重尺度法求得近似解的首项,并用积分方程和非线性Gronwall不等式对所得结果进行误差估计。

Analysis of a finite dimensional perturbed solution for the Kirchhoff equation

We consider the initial-boundary value problem for the Kirchhoff equation describing the transversal vibrations of a clamped string with fixed ends.In the case when the initial displacement and velocity are represented by the finite-dimensional Fourier sine series,a first-term approximate solution is constructed via the method of multiple scales and the error of the approximate solution is estimated by using integral equations and a nonlinear Gronwall inequality.