Time-periodic solutions to a class of quasilinear wave equations
type: Item
instance of: scholarly article
title: Time-periodic solutions to a class of quasilinear wave equations
zbMATH Open document ID: 0813.35048
DOI: 10.1007/BF01816554
author: K. Appert
published in: Archive for Rational Mechanics and Analysis
publication date: 1993-08-29T00:00:00Z
review text: The authors show the existence of a set of functions \(c=c(u)\) for which the quasilinear wave equation \(u_ t - v_ x\), \(v_ t - c^ 2(u)u_ x = 0\) possesses a spatially and temporally periodic solution. The function \(c\) satisfies \(c(-u) = c(u) \geq c_ 0 > 0\), \(c'(u)>0\) for \(u>0\), and \(c'\) has a jump at zero. The solution they construct is shock- free with the only singularities being centered simple waves.
Mathematics Subject Classification ID: 35L40
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 399277
zbMATH Keywords: quasilinear wave equation
reviewed by: Eduard Feireisl
MaRDI profile type: Publication
cites work: Time-periodic solutions to systems of conservation laws
cites work: Convergence of approximate solutions to conservation laws
cites work: Q1081027
full work available at URL: https://doi.org/10.1007/bf01816554
OpenAlex ID: W1965400031
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description: scientific article; zbMATH DE number 399277