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The Riemann problem for a resonant nonlinear system of conservation laws with Dirac-measure solutions*

Published online by Cambridge University Press:  14 November 2011

Jiaxin Hu
Jiaxin Hu
Affiliation:
Young Scientists Laboratory of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, P.R. China
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Extract

The Riemann problem for a resonant nonlinear system of conservation laws is considered here. The Riemann solution was constructed by employing the viscosity approximation approach. One kind of new discontinuity, which is called the Dirac-contact wave, appeared in the Riemann solution. Because the strict hyperbolicity as well as the genuine nonlinearity of the system considered failed, the solution we obtained in this paper is not unique for some initial data. An additional condition was explored to guarantee the uniqueness of the Riemann problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 1 , 1998 , pp. 81 - 94
Copyright
Copyright © Royal Society of Edinburgh 1998

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