Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. I.
type: Item
instance of: scholarly article
title: Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. I.
zbMATH Open document ID: 1117.35045
author: D. L. Tkachev
author: L. O. Baldan
author: A. M. Blokhin
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-05-04T00:00:00Z
review text: The authors consider the mathematical model of a viscous gas consisting of the Navier-Stokes equations for a compressible fluid together with the Gibbs relation. A shock wave is treated as a strong discontinuity. The authors suggest such additional boundary conditions that a modified linear problem does not admit Hadamar-type ill-posedness examples.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 5149571
zbMATH Keywords: well-posedness
zbMATH Keywords: initial-boundary-value problem
zbMATH Keywords: stability of shock waves
zbMATH Keywords: Lyapunov's stability
zbMATH Keywords: Gibbs relation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.08.006
OpenAlex ID: W1988446803
cites work: Q5699257
cites work: Hyperbolic systems of conservation laws II
cites work: Q3247330
cites work: Q3844581
cites work: Solutions in the large for nonlinear hyperbolic systems of equations
cites work: Decay of solutions of systems of hyperbolic conservation laws
cites work: Global solutions for an extended class of hyperbolic systems of conservation laws
cites work: On the structure of magnetohydrodynamic shock waves
cites work: On the structure of magnetohydrodynamic shock waves. II
cites work: Q4046493
cites work: Q5566685
cites work: Q3925254
cites work: Uniqueness of the classical solution of a mixed problem for equations of gas dynamics with boundary conditions on the shock wave
cites work: The stability of multidimensional shock fronts
cites work: The existence of multidimensional shock fronts
cites work: Compressible fluid flow and systems of conservation laws in several space variables
cites work: Q4222728
cites work: Q4220322
cites work: Q4746129
cites work: On stability of shock waves in magnetohydrodynamics with anisotropic pressure
cites work: The Existence and Limit Behavior of the One-Dimensional Shock Layer
cites work: Viscous and inviscid stability of multidimensional planar shock fronts
cites work: Q4151274
cites work: Q4362094
cites work: Shock waves for compressible navier‐stokes equations are stable
cites work: Q3318196
cites work: Q3751991
cites work: Global well-posedness of the Cauchy problem for the Navier-Stokes equations of nonisentropic flow with discontinuous initial data
cites work: Numerical Computation of Two-Dimensional Viscous Blunt Body Flows with an Impinging Shock
cites work: Q4527371
cites work: On stability of shock waves in a compressible viscous heat conducting gas
cites work: Q5735118
cites work: Q5577494
cites work: On a modified shock front problem for the compressible Navier-Stokes equations
cites work: Q5489592
cites work: Q3995626
cites work: Q3328137
DOI: 10.1016/J.JMAA.2006.08.006
description: scientific article; zbMATH DE number 5149571