The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics
type: Item
instance of: scholarly article
title: The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics
zbMATH Open document ID: 1027.35065
DOI: 10.1016/S0362-546X(02)00123-2
author: Yue-Jun Peng
author: Tatsien Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: It is proved that the \(C^0\) boundedness implies the global existence and uniqueness of \(C^1\) solutions to mixed initial-boundary value problems for linearly degenerate, reducible quasilinear hyperbolic systems with nonlinear boundary conditions. It is shown by an example that the \(C^0\) norm of the solution may blow up in finite time. This gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves.
reviewed by: Mersaid Aripov
Mathematics Subject Classification ID: 35L50
Mathematics Subject Classification ID: 35L80
Mathematics Subject Classification ID: 35A21
zbMATH DE Number: 1879968
zbMATH Keywords: linearly degenerate system
zbMATH Keywords: formation of singularity
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: nonlinear hyperbolic waves
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00123-2
OpenAlex ID: W1971168216
description: scientific article; zbMATH DE number 1879968