Transport equations for waves in a half space

Communications in Partial Differential Equations

Volumn 22, Issue 11-12, 1997, Pages 1869-1910

  Ryzhik, Leonid ^a   Papanicolaou, George C ^a   Keller, Joseph B ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001234945     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Yu. Barabanenkov, A. Vinogradov, Yu. Kravtsov and V. Tatarskii, Application of the theory of multiple scattering of waves to the derivation of the radiative transfer equation for a statistically inhomogeneous medium, Radiofizika, 15 1972, 1852-1860. English translation pp. 1420-1425.
2. N. Bleistein, Mathematical Methods for Wave Phenomena, Academic Press, 1984.
3. G. Frankfort, F. Murat, Oscillations and energy densities in the wave equation, Comm. PDEs, 17, 1992, 1785-1865.
4. P. Gérard, Microlocal defect measures, Comm. PDEs, 16, 1991, 1761-1794.
5. P. Gérard, Mesures Semi-Classiques et Ondes de Bloch, Sém. Ecole Polytechnique, exposé XVI, 1990-91, 1-19.
6. P. Gérard, E. Leichtnam, Ergodic properties of eigenfunctions for the Dirichlet problem, Duke Math. J., 71, 1993, 559-607.
7. P. Gérard, P. Markovich, N. Mauser and F. Poupaud, Homogenization limits and Wigner transforms, Comm.Pure Appl. Math., 50, 1997, 323-380.
8. J.B. Keller and R. Lewis, Asymptotic methods for partial differential equations: The reduced wave equation and Maxwell's equations, in Surveys in applied mathematics, eds. J.B. Keller, D. McLaughlin and G. Papanicolaou, Plenum Press, New York, 1995.
9. C.W. Law and K. Watson, Radiation transport along curved ray paths, Jour. Math. Phys., 11, 1970, 3125-3137.
10. P.L. Lions and T. Paul, Sur les Mesures de Wigner, Revista Mat. Iberoamericana, 9, 1993, 553-618.
11. L. Miller. Réfraction d'ondes semi-classiques par des interfaces franches, C. R. Acad. Sci. Paris, Série I, 1997, to appear.
12. L. Miller, Short Waves Through Thin Interfaces and 2-microclocal measures, Journées Equations aux Dérivées Partielles, Saint-Jean-de-Monts, 1997.
13. L. Miller, Propagation d'ondes semi-classiques à travers une interface et mesures 2-microlocales, Doctorat de l'École Polytechnique, Palaiseau, 1996.
14. P. Sheng Introduction to wave scattering, localization, and mesoscopic phenomena, Academic Press, San Diego, 1995.
15. L. Ryzhik, G. Papanicolaou and J. Keller, Transport equations for elastic and other waves in random media, Wave Motion, 24, 1996, 327-370.
16. L. Ryzhik, G. Papanicolaou and J. Keller, Boundary conditions for transport equations for waves in random media, in preparation.
17. L. Schwartz, Théorie des Distributions, Herman, Paris, 1966.
18. L. Tartar, H-measures, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh, 115A, 1990, 193-230.
19. E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev., 40, 1932, 749-759.