TY - JOUR
T1 - Solutions of a nonhyperbolic pair of balance laws
AU - Sever, Michael
PY - 2005/1
Y1 - 2005/1
N2 - We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, non-hyperbolic 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.
AB - We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, non-hyperbolic 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.
KW - Incompressible two-fluid flow
KW - Nonhyperbolic balance laws
UR - http://www.scopus.com/inward/record.url?scp=15744381291&partnerID=8YFLogxK
U2 - 10.1051/m2an:2005003
DO - 10.1051/m2an:2005003
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AN - SCOPUS:15744381291
SN - 0764-583X
VL - 39
SP - 37
EP - 58
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
IS - 1
ER -