Delta shock waves for the chromatography equations as self-similar viscosity limits

Author:
Meina Sun

Journal:
Quart. Appl. Math. **69** (2011), 425-443

MSC (2000):
Primary 35L65, 35L67, 35B30

DOI:
https://doi.org/10.1090/S0033-569X-2011-01207-3

Published electronically:
April 5, 2011

MathSciNet review:
2850739

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Riemann problem for the changed form of the chromatography system is considered here. It can be shown that the delta shock wave appears in the Riemann solution for exactly specified initial states. The generalized Rankine-Hugoniot relation of the delta shock wave is derived in detail. The existence and uniqueness of solutions involving the delta shock wave for the Riemann problem is proven by employing the self-similar viscosity vanishing approach.

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Additional Information

**Meina Sun**

Affiliation:
School of Mathematics and Information, Ludong University, Yantai 264025, People’s Republic of China and Laboratory of Mathematics Physics, Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China

Email:
smnwhy0350@163.com

DOI:
https://doi.org/10.1090/S0033-569X-2011-01207-3

Keywords:
Delta shock wave; Riemann problem; viscosity method; Temple class; chromatography system; hyperbolic conservation laws

Received by editor(s):
October 8, 2009

Published electronically:
April 5, 2011

Additional Notes:
This work is partially supported by the National Natural Science Foundation of China (10901077), the China Postdoctoral Science Foundation (201003504, 20090451089) and the Shandong Provincial Doctoral Foundation (BS2010SF006).

Article copyright:
© Copyright 2011
Brown University

The copyright for this article reverts to public domain 28 years after publication.