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Exchange of conserved quantities in nonhyperbolic systems--An example


Author: Michael Sever
Journal: Proc. Amer. Math. Soc. 129 (2001), 3671-3681
MSC (2000): Primary 35L65, 35L67
DOI: https://doi.org/10.1090/S0002-9939-01-06316-X
Published electronically: July 10, 2001
MathSciNet review: 1860502
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Abstract | References | Similar Articles | Additional Information

Abstract:

The velocity function associated with a smooth solution of ``zero pressure gas dynamics'' satisfies Burgers equation. Indeed an elementary generalization holds for scalar conservation laws. Weak solutions, however, are compatible in this respect only under special conditions on the initial density function. Our result depends on the uniform convexity of the flux function associated with the scalar equation, and on the entropy condition applied to both systems.


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Additional Information

Michael Sever
Affiliation: Department of Mathematics, The Hebrew University, Jerusalem, Israel
Email: sever@math.huji.ac.il

DOI: https://doi.org/10.1090/S0002-9939-01-06316-X
Received by editor(s): May 1, 2000
Published electronically: July 10, 2001
Additional Notes: This research was partially supported by the Texas Advanced Research Program under grant 00365-2102-ARP
Communicated by: Suncica Canic
Article copyright: © Copyright 2001 American Mathematical Society