The Fourier Method (for the Vibrating String)

  • Vladimir I. Arnold
Part of the Universitext book series (UTX)

Abstract

Consider the periodic boundary-value problem for the vibrating string:
$$ {u_{tt}}= {a^2}{u_{xx}},x \in {S^1} = \mathbb{R}/2\pi \mathbb{Z}$$
(5.1)
$$ u{\backslash _{t = 0}} = \varphi \left( x \right),{u_t}{\backslash _{t = 0}} = \psi (x) $$
(5.2)
.

Keywords

Manifold Radon Lution 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
    • 2
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.CEREMADEUniversité de Paris-DauphineParis Cedex 16France

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