Initial boundary value problems for quasilinear symmetric hyperbolic systems with characteristic boundary
type: Item
instance of: scholarly article
title: Initial boundary value problems for quasilinear symmetric hyperbolic systems with characteristic boundary
zbMATH Open document ID: 1203.35166
published in: Frontiers of Mathematics in China
publication date: 2010-09-22T00:00:00Z
review text: The author considers the quasilinear initial-boundary-value symmetric hyperbolic first-order system \[ \alpha_0(x,u)\partial_{t}u + \sum_{i=1}^n{\alpha_i(x,u)\partial_{x_i}u} = f(x,u), \] \(x\in\mathbb R^{n}\), \(u\in\mathbb R^N\), \((t,x)\in[0,h]\times\Omega\subset\mathbb R^{n+1}\), \(f\) and \(\partial\Omega\) are sufficiently smooth. Initial condition is homogeneous (without loss of generality), boundary condition is \(Mu=0\). Other assumptions deal with properties of \(\alpha_i\) and the boundary. Existence of the unique smooth time-local solution is proved. The technique extends the theory of linear symmetric hyperbolic systems to the nonlinear case. Applications to gas dynamics are described.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L50
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 5790128
zbMATH Keywords: existence and uniqueness of smooth solution
author: Shuxing Chen
MaRDI profile type: Publication
full work available at URL: s11464-007-0006-5
OpenAlex ID: W1946799328
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DOI: 10.1007/S11464-007-0006-5
description: scientific article; zbMATH DE number 5790128