Structural stability and data dependence for fully nonlinear hyperbolic mixed problems
type: Item
instance of: scholarly article
title: Structural stability and data dependence for fully nonlinear hyperbolic mixed problems
zbMATH Open document ID: 0801.35083
DOI: 10.1007/BF00381277
author: H. Beirão da Veiga
published in: Archive for Rational Mechanics and Analysis
publication date: 1992-12-14T00:00:00Z
review text: Using the results of [the author, Commun. Pure Appl. Math. 46, No. 2, 221-259 (1993; Zbl 0791.35102)] the author proves continuous dependence of the solutions of nonlinear second order hyperbolic initial boundary value problems \[ \partial^ 2_ t u- \partial_ i(a_ i(\nabla u))= f\quad\text{in }\Omega\times [0,T], \] \[ a_ i(\nabla u)\nu_ i+ b(u)=g\quad\text{in }\partial\Omega\times [0,T],\;u(0)= u_ 0,\;\partial_ t u(0)= u_ 1, \] where \(\Omega\subset\mathbb{R}^ n\) is a bounded domain with smooth boundary and unit outward normal \((\nu_ 1,\dots,\nu_ n)\) to \(\partial\Omega\), on the data \(a_ i\), \(b\), \(f\), \(g\), \(u_ 0\) and \(u_ 1\).
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 78048
zbMATH Keywords: nonlinear second order hyperbolic initial boundary value problems
reviewed by: Lutz Recke
MaRDI profile type: Publication
cites work: Perturbation theory and well-posedness in Hadamard's sense of hyperbolic initial-boundary value problems
cites work: Perturbation theorems for linear hyperbolic mixed problems and applications to the compressible euler equations
cites work: On the mixed problem for some quasilinear hyperbolic system with fully nonlinear boundary condition
cites work: On a local existence theorem of Neumann problem for some quasilinear hyperbolic system of 2nd order
full work available at URL: https://doi.org/10.1007/bf00381277
OpenAlex ID: W2172192901
description: scientific article; zbMATH DE number 78048