Kirchhoff方程有限维摄动解的分析

粟端;江新华*

北京化工大学学报(自然科学版) ›› 2010, Vol. 37 ›› Issue (5) : 135-138.

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北京化工大学学报(自然科学版) ›› 2010, Vol. 37 ›› Issue (5) : 135-138.
管理与数理科学

Kirchhoff方程有限维摄动解的分析

  • 粟端;江新华*
作者信息 +

Analysis of a finite dimensional perturbed solution for the Kirchhoff equation

  • SU Duan;JIANG XinHua
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摘要

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。

Abstract

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.

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粟端;江新华*. Kirchhoff方程有限维摄动解的分析[J]. 北京化工大学学报(自然科学版), 2010, 37(5): 135-138
SU Duan;JIANG XinHua. Analysis of a finite dimensional perturbed solution for the Kirchhoff equation[J]. Journal of Beijing University of Chemical Technology, 2010, 37(5): 135-138

参考文献

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