Stability of a resonant system of conservation laws modeling polymer flow with gravitation

Journal of Differential Equations

Volumn 170, Issue 2, 2001, Pages 344-380

  Klingenberg, Christian ^a   Risebro, Nils Henrik ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Conservation laws; stability; non strictly hyperbolic

Indexed keywords

EID: 0035285314     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3826     Document Type: Article

References (23)

1. ∞ data. J. Differential Equations. 140:1997;161-185.
2. Bressan A., Colombo R. The semigroup generated by 2×2 systems of conservation laws. Arch. Rational Mech. 133:1995;1-75.
3. Dahl O., Johansen T., Tveito A., Winther R. Multicomponent chromatography in a two phase enviroment. SIAM J. Appl. Math. 52:1992;65-104.
4. Gimse T., Risebro N. H. Riemann problems with discontinuous flux functions. Third International Conference on Hyperbolic Problems, Theory Numerical Methods and Applications. 1991;Studentlitteratur/Chartwell-Bratt. p. 488-452.
5. Gimse T., Risebro N. H. Solution of the Cauchy problem for a conservation law with a discontinuous flux function. SIAM J. Math. Anal. 23:1992;635-648.
6. Holden H., Holden L., Høegh-Krohn R. A numerical method for first order nonlinear scalar conservation laws. Comput. Math. Appl. 15:1988;595-602.
7. E. Isaacson, Global solution of a Riemann problem for a non-strictly hyperbolic system of conservation laws arising in enahanced oil recovery, preprint, Rockefeller University, New York, 1981.
8. Isaacson E., Temple B. Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52:1992;1260-1278.
9. Isaacson E., Temple B. Convergence of the 2× Godunov method for a general resonant nonlinear balance law. SIAM J. Appl. Math. 55:1995;625-640.
10. H. K. Jenssen, private communication.
11. K. Karlsen, and, N. H. Risebro, Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. Available at, http://www.math.ntnu.no/conservation/2000/035.ps .
12. R. A. Klausen, and, N. H. Risebro, Well posedness of a 2×2 system of resonant conservation laws, in, Proc. of the 8th International Conference on Hyperbolic Problems, Zürich, 1998.
13. Klausen R. A., Risebro N. H. Stability of conservation laws with discontinuous coefficients. J. Differential Equations. 157:1999;41-60.
14. Klingenberg C., Risebro N. H. Convex conservation laws with discontinuous coefficients, existence, uniqueness and asymtotic behavior. Comm. Partial Differential Equations. 20:1995;1959-1990.
15. Kružkov S. N. First order quasilinear equation in several independent variables. Mat. Sb. 10:1970;217-243.
16. Kuznetsov N. N. Accuracy of some approximate methods for computing the weak solutions of a first order quasilinear equation. USSR Comput. Math. Math. Phys. 16:1976;105-119.
17. Longwai L., Temple B., Jinghua W. Suppression of oscillations in Godunov's method for a resonant non-strictly hyperbolic system. SIAM J. Numer. Anal. 32:1995;841-864.
18. L. Longwai, B. Temple, and, J. Wang, Uniqueness and continuous dependence for a resonant non-strictly hyperbolic system, unpublished note.
19. Oleinik O. A. Discontinuous solutions of nonlinear differential equations. Trans. Amer. Math. Soc. 26:1963;95-172.
20. Smoller J. Shock Waves and Reaction-Diffusion Equations. 1995;Springer-Verlag, New York.
21. Temple B. Global solution of the Caucy problem for a 2×2 non-strictly hyperbolic system of conservation laws. Adv. Appl. Math. 3:1982;335-375.
22. Tveito A., Winther R. Existence, uniqueness and continuous dependence for a system of conservation laws modeling polymer flooding. SIAM J. Math. Anal. 22:1991;905-933.
23. Wagner D. Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions. J. Differential Equations. 68:1987;118-136.