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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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