Solutions of a nonhyperbolic pair of balance laws

Michael Sever

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • Volume: 39, Issue: 1, page 37-58
  • ISSN: 0764-583X

Abstract

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We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome, however, by introducing an alternative “solution” satisfying both components of the initial data and an approximate form of a corresponding linearized system.

How to cite

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Sever, Michael. "Solutions of a nonhyperbolic pair of balance laws." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.1 (2005): 37-58. <http://eudml.org/doc/245692>.

@article{Sever2005,
abstract = {We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome, however, by introducing an alternative “solution” satisfying both components of the initial data and an approximate form of a corresponding linearized system.},
author = {Sever, Michael},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonhyperbolic balance laws; incompressible two-fluid flow; algorithm; smooth solutions; incompressible two-phase flow; hyperbolic system},
language = {eng},
number = {1},
pages = {37-58},
publisher = {EDP-Sciences},
title = {Solutions of a nonhyperbolic pair of balance laws},
url = {http://eudml.org/doc/245692},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Sever, Michael
TI - Solutions of a nonhyperbolic pair of balance laws
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 1
SP - 37
EP - 58
AB - We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome, however, by introducing an alternative “solution” satisfying both components of the initial data and an approximate form of a corresponding linearized system.
LA - eng
KW - nonhyperbolic balance laws; incompressible two-fluid flow; algorithm; smooth solutions; incompressible two-phase flow; hyperbolic system
UR - http://eudml.org/doc/245692
ER -

References

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  9. [9] B.L. Keyfitz, M. Sever and F. Zhang, Viscous singular shock structure for a nonhyperbolic two-fluid model. Nonlinearity 17 (2004) 1731–1747. Zbl1077.35091
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