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Global versus local admissibility criteria for dynamic phase boundaries

Published online by Cambridge University Press:  14 November 2011

Haitao Fan
Haitao Fan
Affiliation:
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Geogia 30332, U.S.A.
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Synopsis

The nonuniqueness of solutions of Riemann problems for a system of conservation laws of mixed type which are admissible according to kinetic relation criteria or travelling wave criteria is proved. The above-mentioned admissibility criteria all consist of local restrictions on points of discontinuity of weak solutions. An example is given which has more than one solution admissible by these local admissibility criteria, but has only one solution, the one-phase solution, satisfying the vanishing viscosity criterion. The entropy rate criterion, however, prefers the two-phase solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 5 , 1993 , pp. 927 - 944
Copyright
Copyright © Royal Society of Edinburgh 1993

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