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A model for peak formation in the two-phase equations


Authors: Björn Sjögreen, Katarina Gustavsson and Reynir Levi Gudmundsson
Journal: Math. Comp. 76 (2007), 1925-1940
MSC (2000): Primary 76T25, 65M99, 35L60
DOI: https://doi.org/10.1090/S0025-5718-07-01992-8
Published electronically: May 30, 2007
MathSciNet review: 2336274
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Abstract | References | Similar Articles | Additional Information

Abstract: We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.


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Additional Information

Björn Sjögreen
Affiliation: Royal Institute of Technology, 100 44 Stockholm, Sweden
Address at time of publication: Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-550, Livermore, California 94551
Email: sjogreen2@llnl.gov

Katarina Gustavsson
Affiliation: Royal Institute of Technology, 100 44 Stockholm, Sweden
Email: katarina@nada.kth.se

Reynir Levi Gudmundsson
Affiliation: Royal Institute of Technology, 100 44 Stockholm, Sweden
Email: rlg@nada.kth.se

DOI: https://doi.org/10.1090/S0025-5718-07-01992-8
Received by editor(s): June 20, 2005
Received by editor(s) in revised form: June 4, 2006
Published electronically: May 30, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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