# Solutions of a nonhyperbolic pair of balance laws

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

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topSever, 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] 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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