Convergence of a relaxation approximation to a boundary value problem for conservation laws

Communications in Partial Differential Equations

Volumn 26, Issue 7-8, 2001, Pages 1235-1252

  Natalini, Roberto ^a   Terracina, Andrea ^b  

^a CNR   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011571725     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-100106133     Document Type: Article

References (29)

1. Aregba-Driollet, D.; Natalini, R. Discrete kinetic schemes for multidimensional conservation laws. Technical Report 22, Quaderno IAC, to appear in SIAM J. Num. Anal. 1997.
2. Bardos, C.; le Roux, A.Y.; Nédélec, J.-C. First order quasilinear equations with boundary conditions. Comm. Partial Differential Equations 1979, 4(9), 1017-1034.
3. Bianchini, S. On a Glimm Type Functional for a special Jin-Xin Relaxation Model. Preprint SISSA, 1999.
4. Bouchut, F. Construction of BGK models with a family of kinetic entropies for a given system of conservation laws. J. Statist. Phys. 1999, 95(1-2), 113-170.
5. Bressan, A.; shen, W.; BV estimates for multicomponent chromatography with relaxation. Technical report, SISSA, 1999.
6. Chen, G.-Q.; Levermore, C.; Liu, T.P. Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 1994, 47, 830-1994.
7. Collet, J.F.; Rascle, M. Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography. Z. Angew. Math. Phys. 1996, 47, 409-1996.
8. James, F. Convergence results for some conservation laws with a reflux boundary condition and a relaxation term arising in chemical engineering. SIAM J. Math. Anal. 1998. in press.
9. Jin, S.; Xin, Z. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 1995, 48, 277-1995.
10. Katsoulakis, M.A.; Tzavaras, A.E. Contractive relaxation systems and the scalar multidimensional conservation law. Comm. Partial Differential Equations 1997, 22(1-2), 195-233.
11. S.N. Kružkov. First order quasilinear equations in several independent variables. Mat. Sb. 1970, 81, 255-1970.
12. Math. USSR Sb, 1970, 10, 243-1970.
13. Liu, H.; Yong, W.A. Admissible boundary conditions and stability of boundary-layers for a hyperbolic relaxation system. Preprint 1999.
14. Liu, T.-P. Hyperbolic conservation laws with relaxation. Comm. Math. Phys. 1987, 108, 175-1987.
15. Natalini, R. Convergence to equilibrium for the relaxation approximations of conservation laws. Comm. Pure Appl. Math. 1996, 49(8), 795-823.
16. Natalini, R. A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws. J. Differential Equations 1998, 148(2), 292-317.
17. Natalini, R. Recent results on hyperbolic relaxation problems. In Analysis of systems of conservation laws (Aachen, 1997), pages 128-198. Chapman & Hall/CRC, Boca Raton, FL, 1999.
18. Natalini, R.; Tesei, A. Existence of solutions and relaxation properties of the Barenblatt model of non-equilibrium for a two phase flow. Arch. Rational Mech. Anal. 1999, 150(4), 349-367.
19. Nishibata, S. The initial-boundary value problems for hyperbolic conservation laws with relaxation. J. Differential Equations 1996, 130(1), 100-126.
20. Nouri, A.; Omrane, A.; Vila, J.P. Boundary conditions for scalar conservation laws from a kinetic point of view. J. Statist. Phys. 1999, 94(5-6), 779-804.
21. Perthame B.; Tadmor, E. A kinetic equation with kinetic entropy functions for scalar conservation laws. Comm. Math. Phys. 1991, 136, 517-1991.
22. Serre, D. Relaxation semi-linéaire et cinétique des systèmes de lois de conservation, to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire.
23. Terracina, A. Comparison properties for scalar conservation laws with boundary conditions. Nonlinear Anal. 1997, 28(4), 633-653.
24. Terracina, A. Applicazioni di teoremi di confronto per leggi di conservazione con condizioni al bordo. PhD thesis, Università degli Studi di Roma"La Sapienza", 1998.
25. Tveito, A.; Winther, R. On the rate of convergence to equilibrium for a system of conservation laws with a relaxation term. SIAM J. Math. Anal. 1997, 28, 161-1997.
26. Wang W.C.; Xin, Z. Asymptotic limit of initial-boundary value problems for conservation laws with relaxational extensions. Comm. Pure Appl. Math. 1998, 51(5), 505-535.
27. J. Whitham. Linear and nonlinear waves. Wiley, New York, 1974.
28. Yong, W.A. Boundary conditions for hyperbolic systems with stiff source terms. Technical report, IWR, University of Heidelberg, 1997.
29. Yong, W.A. Singular perturbations of first-order hyperbolic systems with stiff source terms. J. Differential Equations 1999, 155(1), 89-132.