Relaxation limit for hyperbolic systems in chromatography
HTML articles powered by AMS MathViewer
- by Yun-Guang Lu
- Proc. Amer. Math. Soc. 130 (2002), 3579-3583
- DOI: https://doi.org/10.1090/S0002-9939-02-06667-4
- Published electronically: June 18, 2002
- PDF | Request permission
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).References
- Alberto Bressan and Wen Shen, BV estimates for multicomponent chromatography with relaxation, Discrete Contin. Dynam. Systems 6 (2000), no. 1, 21–38. MR 1739591, DOI 10.3934/dcds.2000.6.21
- Gui Qiang Chen, Hyperbolic systems of conservation laws with a symmetry, Comm. Partial Differential Equations 16 (1991), no. 8-9, 1461–1487. MR 1132792, DOI 10.1080/03605309108820806
- Gui Qiang Chen, C. David Levermore, and Tai-Ping Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994), no. 6, 787–830. MR 1280989, DOI 10.1002/cpa.3160470602
- Gui Qiang Chen and Tai-Ping Liu, Zero relaxation and dissipation limits for hyperbolic conservation laws, Comm. Pure Appl. Math. 46 (1993), no. 5, 755–781. MR 1213992, DOI 10.1002/cpa.3160460504
- Heinrich Freistühler, A standard model of generic rotational degeneracy, Nonlinear hyperbolic equations—theory, computation methods, and applications (Aachen, 1988) Notes Numer. Fluid Mech., vol. 24, Friedr. Vieweg, Braunschweig, 1989, pp. 149–158. MR 991360
- Barbara L. Keyfitz and Herbert C. Kranzer, A system of nonstrictly hyperbolic conservation laws arising in elasticity theory, Arch. Rational Mech. Anal. 72 (1979/80), no. 3, 219–241. MR 549642, DOI 10.1007/BF00281590
- A. Kurganov and E. Tadmor, Stiff systems of hyperbolic conservation laws: convergence and error estimates, SIAM J. Math. Anal. 28 (1997), no. 6, 1446–1456. MR 1474223, DOI 10.1137/S0036141096301488
- Tai-Ping Liu and Ching-Hua Wang, On a nonstrictly hyperbolic system of conservation laws, J. Differential Equations 57 (1985), no. 1, 1–14. MR 788420, DOI 10.1016/0022-0396(85)90068-3
- 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.
- Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
- Aslak Tveito and Ragnar Winther, On the rate of convergence to equilibrium for a system of conservation laws with a relaxation term, SIAM J. Math. Anal. 28 (1997), no. 1, 136–161. MR 1427731, DOI 10.1137/S0036141094263755
- Athanasios E. Tzavaras, Materials with internal variables and relaxation to conservation laws, Arch. Ration. Mech. Anal. 146 (1999), no. 2, 129–155. MR 1718478, DOI 10.1007/s002050050139
Bibliographic 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
- Received by editor(s): March 24, 2001
- Published electronically: June 18, 2002
- Communicated by: David S. Tartakoff
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1920037