Free access
Issue
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
Page(s) 961 - 987
DOI http://dx.doi.org/10.1051/m2an:2004046
Published online 15 December 2004
  1. G. Bal, On the self-averaging of wave energy in random media. SIAM Multiscale Model. Simul. 2 (2004) 398–420. [CrossRef]
  2. G. Bal and L. Ryzhik, Time reversal for classical waves in random media. C. R. Acad. Sci. Paris I 333 (2001) 1041–1046.
  3. G. Bal and L. Ryzhik, Time reversal and refocusing in random media. SIAM J. Appl. Math. 63 (2003) 1475–1498. [CrossRef] [MathSciNet]
  4. G. Bal, A. Fannjiang, G. Papanicolaou and L. Ryzhik, Radiative transport in a periodic structure. J. Statist. Phys. 95 (1999) 479–494. [CrossRef] [MathSciNet]
  5. G. Bal, G. Papanicolaou and L. Ryzhik, Radiative transport limit for the random Schrödinger equations. Nonlinearity 15 (2002) 513–529. [CrossRef] [MathSciNet]
  6. G. Bal, G. Papanicolaou and L. Ryzhik, Self-averaging in time reversal for the parabolic wave equation. Stochastics Dynamics 4 (2002) 507–531. [CrossRef]
  7. G. Bal, T. Komorowski and L. Ryzhik, Self-averaging of the Wigner transform in random media. Comm. Math. Phys. 242 (2003) 81–135. [MathSciNet]
  8. W. Bao, S. Jin and P.A. Markowich, On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime. J. Comp. Phys. 175 (2002) 487–524. [CrossRef] [MathSciNet]
  9. C. Bardos and M. Fink, Mathematical foundations of the time reversal mirror. Asymptot. Anal. 29 (2002) 157–182. [MathSciNet]
  10. P. Blomgren, G. Papanicolaou and H. Zhao, Super-resolution in time-reversal acoustics. J. Acoust. Soc. Am. 111 (2002) 230–248. [CrossRef] [PubMed]
  11. S. Chandrasekhar, Radiative Transfer. Dover Publications, New York (1960).
  12. J.F. Clouet and J.-P. Fouque, A time-reversal method for an acoustical pulse propagating in randomly layered media. Wave Motion 25 (1997) 361–368. [CrossRef] [MathSciNet]
  13. G.C. Cohen, Higher-order numerical methods for transient wave equations. Scientific Computation, Springer-Verlag, Berlin (2002).
  14. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 6, Springer-Verlag, Berlin (1993).
  15. D.R. Durran, Nunerical Methods for Wave equations in Geophysical Fluid Dynamics. Springer, New York (1999).
  16. L. Erdös and H.T. Yau, Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. Comm. Pure Appl. Math. 53 (2000) 667–735. [CrossRef] [MathSciNet]
  17. M. Fink, Time reversed acoustics. Physics Today 50 (1997) 34–40. [CrossRef]
  18. M. Fink, Chaos and time-reversed acoustics. Physica Scripta 90 (2001) 268–277. [CrossRef]
  19. P. Gérard, P.A. Markowich, N.J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms. Comm. Pure Appl. Math. 50 (1997) 323–380. [CrossRef] [MathSciNet]
  20. F. Golse, S. Jin and C.D. Levermore, The convergence of numerical transfer schemes in diffusive regimes. I. Discrete-ordinate method. SIAM J. Numer. Anal. 36 (1999) 1333–1369. [CrossRef] [MathSciNet]
  21. W. Hodgkiss, H. Song, W. Kuperman, T. Akal, C. Ferla and D. Jackson, A long-range and variable focus phase-conjugation experiment in a shallow water. J. Acoust. Soc. Am. 105 (1999) 1597–1604. [CrossRef]
  22. T.Y. Hou, X. Wu and Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comp. 227 (1999) 913–943. [CrossRef] [MathSciNet]
  23. A. Ishimaru, Wave Propagation and Scattering in Random Media. New York, Academics (1978).
  24. 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, J.B. Keller, D. McLaughlin and G. Papanicolaou Eds., Plenum Press, New York (1995).
  25. P.-L. Lions and T. Paul, Sur les mesures de Wigner. Rev. Mat. Iberoamericana 9 (1993) 553–618. [CrossRef] [MathSciNet]
  26. P. Markowich, P. Pietra and C. Pohl, Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit. Numer. Math. 81 (1999) 595–630. [CrossRef] [MathSciNet]
  27. P. Markowich, P. Pietra, C. Pohl and H.P. Stimming, A Wigner-measure analysis of the Dufort-Frankel scheme for the Schrödinger equation. SIAM J. Numer. Anal. 40 (2002) 1281–1310. [CrossRef] [MathSciNet]
  28. G. Papanicolaou, L. Ryzhik and K. Solna, The parabolic approximation and time reversal. Matem. Contemp. 23 (2002) 139–159.
  29. G. Papanicolaou, L. Ryzhik and K. Solna, Statistical stability in time reversal. SIAM J. App. Math. 64 (2004) 1133–1155. [CrossRef]
  30. F. Poupaud and A. Vasseur, Classical and quantum transport in random media. J. Math. Pures Appl. 82 (2003) 711–748. [CrossRef] [MathSciNet]
  31. L. Ryzhik, G. Papanicolaou and J.B. Keller, Transport equations for elastic and other waves in random media. Wave Motion 24 (1996) 327–370. [CrossRef] [MathSciNet]
  32. H. Sato and M.C. Fehler, Seismic wave propagation and scattering in the heterogeneous earth. AIP series in modern acoustics and signal processing, AIP Press, Springer, New York (1998).
  33. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena. Academic Press, New York (1995).
  34. H. Spohn, Derivation of the transport equation for electrons moving through random impurities. J. Stat. Phys. 17 (1977) 385–412. [CrossRef]
  35. G. Strang, On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 507–517.
  36. F. Tappert, The parabolic approximation method, Lect. notes Phys., Vol. 70, Wave propagation and underwater acoustics. Springer-Verlag (1977).
  37. B.J. Uscinski, The elements of wave propagation in random media. McGraw-Hill, New York (1977).
  38. B.J. Uscinski, Analytical solution of the fourth-moment equation and interpretation as a set of phase screens. J. Opt. Soc. Am. 2 (1985) 2077–2091. [CrossRef]

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