Volume 39, Number 1, January-February 2005
|Page(s)||37 - 58|
|Published online||15 March 2005|
Solutions of a nonhyperbolic pair of balance laws
Department of Mathematics, The Hebrew University,
Jerusalem, Israel. email@example.com
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.
Mathematics Subject Classification: 35M99 / 35Q35 / 76T10
Key words: Nonhyperbolic balance laws / incompressible two-fluid flow.
© EDP Sciences, SMAI, 2005
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