Delta shock waves for the chromatography equations as selfsimilar viscosity limits
Author:
Meina Sun
Journal:
Quart. Appl. Math. 69 (2011), 425443
MSC (2000):
Primary 35L65, 35L67, 35B30
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 RankineHugoniot 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 selfsimilar viscosity vanishing approach.
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 4.
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 C.M.Dafermos, Solutions of the Riemann problem for a class of hyperbolic system of conservation laws by the viscosity method, Arch. Rational Mech. Anal., 52(1973), 19. MR 0340837 (49:5587)
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 M.Mazzotti, Nonclassical composition fronts in nonlinear chromatography  Deltashock, Ind. Eng. Chem. Res. 48(2009), 77337752.
 22.
 M. Mazzotti, A. Tarafder, J. Cornel, F. Gritti, and G. Guiochon, Experimental evidence of a deltashock in nonlinear chromatography, J. Chromatography. A, 1217(2010), 20022012.
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 E.Yu.Panov and V.M.Shelkovich, shock waves as a new type of solutions to system of conservation laws, J. Differential Equations, 228(2006), 4986. MR 2254184 (2007f:35188)
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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:
http://dx.doi.org/10.1090/S0033569X2011012073
PII:
S 0033569X(2011)012073
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.
