EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 35 / No 3 (May-June 2001) ESAIM: M2AN, 35 3 (2001) 463-480 References
Free Access
Issue
ESAIM: M2AN
Volume 35, Number 3, May-June 2001
Page(s) 463 - 480
DOI https://doi.org/10.1051/m2an:2001123
Published online 15 April 2002
  1. A. Bernudez and M.E. Vazquez, Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23 (1994) 1049-1071. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Botchorishvili, B. Perthame and A. Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources. Math. Comp. (to appear). [Google Scholar]
  3. A. Chinnayya and A.Y. Le Roux, A new general Riemann solver for the shallow-water equations with friction and topography. Preprint (1999). [Google Scholar]
  4. V. Cornish, Ocean waves and kindred geophysical phenomena. Cambridge University Press, London (1934). [Google Scholar]
  5. C.M. Dafermos, Hyperbolic conservation laws in continuum physics. Grundlehren der Mathematischen Wissenschaften 325, Springer-Verlag, Berlin (2000) xvi+443 pp. [Google Scholar]
  6. R.F. Dressler, Mathematical solution of the problem of roll-waves in inclined open channels. Comm. Pure Appl. Math. 2 (1949) 149-194. [CrossRef] [MathSciNet] [Google Scholar]
  7. T. Gallouët, J.-M. Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography. AIAA-2001 (to appear). [Google Scholar]
  8. J. Goodman, Stability of the Kuramoto-Sivashinsky and related systems. Comm. Pure Appl. Math. 47 (1994) 293-306. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Gosse, A well-balanced flux-vector splitting scheme desinged for hyperbolic systems of conservation laws with source terms. Comp. Math. Appl. 39 (2000) 135-159. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.M. Greenberg and A.-Y. Le Roux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1-16. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  11. J.K. Hunter, Asymptotic equations for nonlinear hyperbolic waves, in Surveys in Appl. Math. Vol. 2, J.B. Keller, G. Papanicolaou, D.W. McLaughlin, Eds. (1993). [Google Scholar]
  12. H. Jeffreys, The flow of water in an inclined channel of rectangular section. Phil. Mag. 49 (1925) 793-807. [Google Scholar]
  13. S. Jin, A steady-state capturing method for hyperbolic systems with source terms. ESAIM: M2AN (to appear). [Google Scholar]
  14. S. Jin and M. Katsoulakis, Hyperbolic systems with supercharacteristic relaxations and roll waves. SIAM J. Appl. Math. 61 (2000) 271-292 (electronic). [Google Scholar]
  15. Y.J. Kim and A.E. Tzavaras, Diffusive N-waves and metastability in Burgers equation. Preprint. [Google Scholar]
  16. C. Kranenburg, On the evolution of roll waves. J. Fluid Mech. 245 (1992) 249-261. [CrossRef] [MathSciNet] [Google Scholar]
  17. P.D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves. CBMS-NSF Regional Conference Series Appl. Math. 11, Philadelphia (1973). [Google Scholar]
  18. R. LeVeque, Numerical methods for conservation laws. Lect. Math., ETH Zurich, Birkhauser (1992). [Google Scholar]
  19. R.J. LeVeque, Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comp. Phys. 146 (1998) 346-365. [CrossRef] [Google Scholar]
  20. T.P. Liu, Nonlinear stability of shock waves for viscous conservation laws. Memoirs of the AMS 56 (1985). [Google Scholar]
  21. A.N. Lyberopoulos, Asymptotic oscillations of solutions of scalar conservation laws with convexity under the action of a linear excitation. Quart. Appl. Math. XLVIII (1990) 755-765. [Google Scholar]
  22. D.J. Needham and J.H. Merkin, On roll waves down an open inclined channel. Proc. Roy. Soc. Lond. A 394 (1984) 259-278. [CrossRef] [Google Scholar]
  23. O.B. Novik, Model description of roll-waves. J. Appl. Math. Mech. 35 (1971) 938-951. [CrossRef] [MathSciNet] [Google Scholar]
  24. P.L. Roe, Upwind differenced schemes for hyperbolic conservation laws with source terms. Lect. Notes Math. 1270, Springer, New York (1986) 41-51. [Google Scholar]
  25. J.J. Stoker, Water Waves. John Wiley and Sons, New York (1958). [Google Scholar]
  26. J. Whitham, Linear and nonlinear waves. Wiley, New York (1974). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you