Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
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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.

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