A maximum principle for periodic solutions of the telegraph equation
type: Item
instance of: scholarly article
title: A maximum principle for periodic solutions of the telegraph equation
zbMATH Open document ID: 0932.35016
author: Rafael Ortega
author: Aureliano M. Robles-Pérez
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-03-08T00:00:00Z
review text: This paper deals with a maximum principle for the doubly \(2\pi\)-periodic solutions of the telegraph operator defined by \[ {\mathcal L}_\lambda u= u_{tt}- u_{xx}+ cu_t-\lambda u, \] with \(c>0\). It is proved that \({\mathcal L}_\lambda\) satisfies the maximum principle if and only if \(\lambda\in [-\nu,0)\) for some \[ \nu= \nu(c)\in\Biggl({c^2\over 4},{c^2\over 4}+ {1\over 4}\Biggr]. \] Applications of this interesting principle are given to the linear telegraph operator with variable coefficients, and to a method of upper and lower solutions for the periodic solutions of nonlinear telegraph equations, which include the sine-Gordon equation.
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 1217031
zbMATH Keywords: doubly \(2\pi\)-periodic solutions
zbMATH Keywords: method of upper and lower solutions
zbMATH Keywords: sine-Gordon equation
reviewed by: Jean Mawhin
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5921
OpenAlex ID: W2006439460
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DOI: 10.1006/JMAA.1998.5921
description: scientific article; zbMATH DE number 1217031