EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 34 / No 6 (November/December 2000) ESAIM: M2AN, 34 6 (2000) 1203-1231 References
Free Access
Issue
ESAIM: M2AN
Volume 34, Number 6, November/December 2000
Page(s) 1203 - 1231
DOI https://doi.org/10.1051/m2an:2000124
Published online 15 April 2002
  1. R. Abgrall and J.-D. Benamou, Big ray tracing and eikonal solver on unstructured grids: Application to the computation of a multivalued traveltime field in the Marmousi model. Geophysics 64 (1999) 230-239. [CrossRef] [Google Scholar]
  2. J.-D. Benamou, Big ray tracing: Multivalued travel time field computation using viscosity solutions of the eikonal equation. J. Comput. Phys. 128 (1996) 463-474. [CrossRef] [Google Scholar]
  3. J.-D. Benamou, Direct solution of multivalued phase space solutions for Hamilton-Jacobi equations. Comm. Pure Appl. Math. 52 (1999) 1443-1475. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.-D. Benamou, F. Castella, T. Katsaounis and B. Perthame, High frequency limit of the Helmholtz equation. Research report DMA-99-25, Département de Mathématiques et Applications, École Normale Supérieure, Paris (1999). [Google Scholar]
  5. F. Bouchut, On zero pressure gas dynamics, in Advances in kinetic theory and computing, Ser. Adv. Math. Appl. Sci. 22, World Sci. Publishing, River Edge, NJ (1994) 171-190. [Google Scholar]
  6. F. Bouchut and F. James, Équations de transport unidimensionnelles à coefficients discontinus. C. R. Acad. Sci. Paris Sér. I Math. 320 (1995) 1097-1102. [Google Scholar]
  7. F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservation laws and uniqueness. Comm. Partial Differential Equations 24 (1999) 2173-2189. [Google Scholar]
  8. Y. Brenier and L. Corrias, A kinetic formulation for multibranch entropy solutions of scalar conservation laws. Ann. Inst. H. Poincaré 15 (1998) 169-190. [Google Scholar]
  9. Y. Brenier and E. Grenier, Sticky particles and scalar conservation laws. SIAM J. Numer. Anal. 35 (1998) 2317-2328. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Castella, O. Runborg and B. Perthame, High frequency limit of the Helmholtz equation II: Source on a general smooth manifold. Research report, Département de Mathématiques et Applications, École Normale Supérieure, Paris (2000). [Google Scholar]
  11. M. Crandall and P. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1-42. [CrossRef] [MathSciNet] [Google Scholar]
  12. W. E, Yu.G. Rykov and Ya.G. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics. Comm. Math. Phys. 177 (1996) 349-380. [CrossRef] [MathSciNet] [Google Scholar]
  13. B. Engquist, E. Fatemi and S. Osher, Numerical solution of the high frequency asymptotic expansion for the scalar wave equation. J. Comput. Phys. 120 (1995) 145-155. [CrossRef] [MathSciNet] [Google Scholar]
  14. B. Engquist and O. Runborg, Multiphase computations in geometrical optics. J. Comput. Appl. Math. 74 (1996) 175-192. [CrossRef] [MathSciNet] [Google Scholar]
  15. B. Engquist and O. Runborg, Multiphase computations in geometrical optics, in Hyperbolic Problems: Theory, Numerics, Applications, M. Fey and R. Jeltsch Eds., Internat. Ser. Numer. Math. 129, ETH Zentrum, Zürich, Switzerland (1998). [Google Scholar]
  16. P. Gérard, P.A. Markowich, N.J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms. Comm. Pure Appl. Math. 50 (1997) 323-379. [CrossRef] [MathSciNet] [Google Scholar]
  17. L. Gosse and F. James, Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients. Math. Comp. 69 (2000) 987-1015. [Google Scholar]
  18. H. Grad, On the kinetic theory of rarefied gases. Comm. Pure Appl. Math. 2 (1949) 331-407. [Google Scholar]
  19. E. Grenier, Existence globale pour le système des gaz sans pression. C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 171-174. [Google Scholar]
  20. G.-S. Jiang and E. Tadmor, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19 (1998) 1892-1917. [CrossRef] [MathSciNet] [Google Scholar]
  21. J. Keller, Geometrical theory of diffraction. J. Opt. Soc. Amer. 52 (1962) 116-130. [CrossRef] [MathSciNet] [Google Scholar]
  22. R.G. Kouyoumjian and P.H. Pathak, A uniform theory of diffraction for an edge in a perfectly conducting surface. Proc. IEEE 62 (1974) 1448-1461. [Google Scholar]
  23. Yu.A. Kravtsov, On a modification of the geometrical optics method. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 7 (1964) 664-673. [Google Scholar]
  24. R.J. LeVeque, Numerical Methods for Conservation Laws. Birkhäuser (1992). [Google Scholar]
  25. C.D. Levermore, Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83 (1996) 1021-1065. [Google Scholar]
  26. P.-L. Lions and T. Paul, Sur les mesures de Wigner. Rev. Mat. Iberoamericana 9 (1993) 553-618. [CrossRef] [MathSciNet] [Google Scholar]
  27. D. Ludwig, Uniform asymptotic expansions at a caustic. Comm. Pure Appl. Math. 19 (1966) 215-250. [CrossRef] [MathSciNet] [Google Scholar]
  28. S. Osher and C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 28 (1991) 907-922. [CrossRef] [MathSciNet] [Google Scholar]
  29. F. Poupaud and M. Rascle, Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients. Comm. Partial Differential Equations 22 (1997) 337-358. [MathSciNet] [Google Scholar]
  30. O. Runborg, Multiscale and Multiphase Methods for Wave Propagation. Ph.D. thesis, Department of Numerical Analysis and Computing Science, KTH, Stockholm (1998). [Google Scholar]
  31. W.W. Symes, A slowness matching finite difference method for traveltimes beyond transmission caustics. Preprint, Dept. of Computational and Applied Mathematics, Rice University (1996). [Google Scholar]
  32. L. Tartar, H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 193-230. [CrossRef] [MathSciNet] [Google Scholar]
  33. J. van Trier and W.W. Symes, Upwind finite-difference calculation of traveltimes. Geophysics 56 (1991) 812-821. [CrossRef] [Google Scholar]
  34. J. Vidale, Finite-difference calculation of traveltimes. Bull. Seismol. Soc. Amer. 78 (1988) 2062-2076. [Google Scholar]
  35. G.B. Whitham, Linear and Nonlinear Waves. John Wiley & Sons (1974). [Google Scholar]
  36. Y. Zheng, Systems of conservation laws with incomplete sets of eigenvectors everywhere, in Advances in Nonlinear Partial Differential Equations and Related Areas, World Sci. Publishing, River Edge, NJ (1998) 399-426. [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