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Relaxation limit for hyperbolic systems in chromatography


Author: Yun-Guang Lu
Journal: Proc. Amer. Math. Soc. 130 (2002), 3579-3583
MSC (2000): Primary 35L65, 35B40
DOI: https://doi.org/10.1090/S0002-9939-02-06667-4
Published electronically: June 18, 2002
MathSciNet review: 1920037
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Abstract: This paper is concerned with a $2n \times 2n$ nonlinear system which arises in chromatography. The global existence of solutions $(u^{\tau}_{i},v^{\tau}_{i})$ in $ L^{\infty}$ space for a Cauchy problem with initial data is obtained for any fixed $\tau > 0$, and the convergence of $(u^{\tau}_{i},v^{\tau}_{i})$ to its equilibrium state $(u_{i},v_{i})$, governed by a limit system is proved for the case $n=2$ by using the compensated compactness coupled with the framework of Tzavaras (1999).


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  • 1. A. Bressan and W. Shen, Estimates for Multicomponent Chromatography with Relaxation, Discr. Cont. Dyn. Sys., 6(2000), 21-38. MR 2000m:35121
  • 2. G. Q. Chen, Hyperbolic system of conservation laws with asymmetry, Commun. PDE, 16(1991), 1461-1487. MR 92g:35130
  • 3. G. Q. Chen, C.D. Levermore and T. P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47(1994), 787-830. MR 95h:35133
  • 4. G. Q. Chen and T. P. Liu, Zero relaxation and dissipation limits for hyperbolic conservation laws, Comm. Pure Appl. Math., 46(1993), 755-781. MR 94b:35167
  • 5. H. A. Freistühler, Standard model of generic rotational degeneracy, In: Nonlinear Hyperbolic Equations, Theory, Computation Methods and Applications, edited by J. Ballmann and R. Jeltsch, Vieweg, Braunschweig 1989, pp. 149-158. MR 90k:35166
  • 6. B. Keyfitz and H. Kranzer, A system of non strictly hyperbolic conservation laws arising inelasticity, Arch. Rational Mech. Anal., 72(1980), 219-241. MR 80k:35050
  • 7. A. Kurganov and E. Tadmor, Stiff system of hyperbolic conservation laws: Convergence and error estimates, SIAM J. Math. Anal., 28(1997), 6: 1446-1456. MR 98j:35117
  • 8. T. P. Liu and J. H. Wang, On a hyperbolic system of conservation laws which is not strictly hyperbolic, J. Diff. Equs., 57(1985), 1-14. MR 86j:35108
  • 9. H. K. Rhee, R. Aris and N. R. Amundsen, On the theory of multicomponent chromatography, Phil. Trans. Royal. Soc. of London, 267A (1970), 419-455.
  • 10. J. A. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer Verlag, New York-Heidelberg-Berlin (1982). MR 84d:35002
  • 11. A. Tveito and R. Winther, On the rate of convergence to equilibrium for a system of conservation laws including a relaxation term, SIAM J. Math. Anal., 28(1997), 136-161. MR 98a:35087
  • 12. A. Tzavaras, Materials with internal variables and relaxation to conservation laws, Arch. Rational Mech. Anal., 146(1999), 2, 129-155. MR 2000i:74004

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Additional Information

Yun-Guang Lu
Affiliation: Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia, Bogotá, Colombia – and – Department of Mathematics, University of Science and Technology of China, Hefei, People’s Republic of China
Email: yglu@matematicas.unal.edu.co

DOI: https://doi.org/10.1090/S0002-9939-02-06667-4
Keywords: Multicomponent chromatography, relaxation limit, compensated compactness
Received by editor(s): March 24, 2001
Published electronically: June 18, 2002
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society

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