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Solutions of a nonhyperbolic pair of balance laws

Published online by Cambridge University Press:  15 March 2005

Michael Sever
Michael Sever*
Affiliation:
Department of Mathematics, The Hebrew University, Jerusalem, Israel. server@math.huji.ac.il
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Abstract

We describe a constructive algorithm for obtaining smoothsolutions of a nonlinear, nonhyperbolic pair of balance lawsmodeling incompressible two-phase flow in one space dimension andtime. Solutions are found as stationary solutions of a relatedhyperbolic system, based on the introduction of an artificial timevariable.As may be expected for such nonhyperbolic systems, in general thesolutions obtained do not satisfy both components of the giveninitial data. This deficiency may be overcome, however, byintroducing an alternative “solution" satisfying both componentsof the initial data and an approximate form of a correspondinglinearized system.

Keywords

Nonhyperbolic balance lawsincompressible two-fluid flow.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 1 , January 2005 , pp. 37 - 58
Copyright
© EDP Sciences, SMAI, 2005

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