Existence of a weak solution for a quasilinear wave equation with boundary condition
type: Item
instance of: scholarly article
title: Existence of a weak solution for a quasilinear wave equation with boundary condition
zbMATH Open document ID: 1010.35073
author: Alain Hertzog
author: Antoine Mondoloni
published in: Communications on Pure and Applied Analysis
publication date: 2003-05-08T00:00:00Z
review text: The authors prove the existence of a weak solution to the initial-boundary value problem \(w_{tt}=(\sigma(w_{x}))_{x}, x>0,t>0, w_{x}(0,t)=0\) with the initial data having bounded total variation, where \(\sigma (s)=as+bs^{2n+1}, n\geq 1, a>0,b>0. \) The proof depends on three main ingredients: construction of approximate solutions by the Glimm scheme, interaction estimates and decreasing of an appropriate functional.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1833240
zbMATH Keywords: initial data having bounded total variation
zbMATH Keywords: wave interaction
zbMATH Keywords: Riemann problem
zbMATH Keywords: Glimm scheme
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: cpaa.2002.1.191
OpenAlex ID: W4243434858
DOI: 10.3934/CPAA.2002.1.191
description: scientific article; zbMATH DE number 1833240