Free Access
Volume 35, Number 3, May-June 2001
Page(s) 463 - 480
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]
  2. R. Botchorishvili, B. Perthame and A. Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources. Math. Comp. (to appear).
  3. A. Chinnayya and A.Y. Le Roux, A new general Riemann solver for the shallow-water equations with friction and topography. Preprint (1999).
  4. V. Cornish, Ocean waves and kindred geophysical phenomena. Cambridge University Press, London (1934).
  5. C.M. Dafermos, Hyperbolic conservation laws in continuum physics. Grundlehren der Mathematischen Wissenschaften 325, Springer-Verlag, Berlin (2000) xvi+443 pp.
  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]
  7. T. Gallouët, J.-M. Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography. AIAA-2001 (to appear).
  8. J. Goodman, Stability of the Kuramoto-Sivashinsky and related systems. Comm. Pure Appl. Math. 47 (1994) 293-306. [CrossRef] [MathSciNet]
  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]
  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] [MathSciNet]
  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).
  12. H. Jeffreys, The flow of water in an inclined channel of rectangular section. Phil. Mag. 49 (1925) 793-807.
  13. S. Jin, A steady-state capturing method for hyperbolic systems with source terms. ESAIM: M2AN (to appear).
  14. S. Jin and M. Katsoulakis, Hyperbolic systems with supercharacteristic relaxations and roll waves. SIAM J. Appl. Math. 61 (2000) 271-292 (electronic).
  15. Y.J. Kim and A.E. Tzavaras, Diffusive N-waves and metastability in Burgers equation. Preprint.
  16. C. Kranenburg, On the evolution of roll waves. J. Fluid Mech. 245 (1992) 249-261. [CrossRef] [MathSciNet]
  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).
  18. R. LeVeque, Numerical methods for conservation laws. Lect. Math., ETH Zurich, Birkhauser (1992).
  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. [NASA ADS] [CrossRef] [MathSciNet]
  20. T.P. Liu, Nonlinear stability of shock waves for viscous conservation laws. Memoirs of the AMS 56 (1985).
  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.
  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]
  23. O.B. Novik, Model description of roll-waves. J. Appl. Math. Mech. 35 (1971) 938-951. [CrossRef] [MathSciNet]
  24. P.L. Roe, Upwind differenced schemes for hyperbolic conservation laws with source terms. Lect. Notes Math. 1270, Springer, New York (1986) 41-51.
  25. J.J. Stoker, Water Waves. John Wiley and Sons, New York (1958).
  26. J. Whitham, Linear and nonlinear waves. Wiley, New York (1974).

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