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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.
@article{M2AN_2005__39_1_37_0,
author = {Sever, Michael},
title = {Solutions of a nonhyperbolic pair of balance laws},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {37--58},
publisher = {EDP-Sciences},
volume = {39},
number = {1},
year = {2005},
doi = {10.1051/m2an:2005003},
mrnumber = {2136199},
zbl = {1080.35092},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005003/}
}
TY - JOUR AU - Sever, Michael TI - Solutions of a nonhyperbolic pair of balance laws JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2005 SP - 37 EP - 58 VL - 39 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005003/ DO - 10.1051/m2an:2005003 LA - en ID - M2AN_2005__39_1_37_0 ER -
%0 Journal Article %A Sever, Michael %T Solutions of a nonhyperbolic pair of balance laws %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2005 %P 37-58 %V 39 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005003/ %R 10.1051/m2an:2005003 %G en %F M2AN_2005__39_1_37_0
Sever, Michael. Solutions of a nonhyperbolic pair of balance laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 1, pp. 37-58. doi: 10.1051/m2an:2005003
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