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Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type

Published online by Cambridge University Press:  14 November 2011

Michael Shearer
Michael Shearer
Affiliation:
Department of Mathematics, Duke University, Durham, North Carolina 27706, U.S.A.
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Synopsis

The following system of conservation laws is considered:

where σ: ℝ→ℝ is a smooth function monotonically increasing except in an interval. Two criteria for the admissibility of shocks are shown to be independent in the sense that there are shocks satisfying each and violating the other. This contrasts with the corresponding situation for strictly hyperbolic systems (σ'(u)>0 for all u), for which the two criteria are equivalent.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 3-4 , 1983 , pp. 233 - 244
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

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