Skip to main content
Log in

Steady-state wave propagation in homogeneous anisotropic media

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Avila, G. S. S., & C. H. Wilcox, The near-field behavior of the Green's matrix in anisotropic wave motion. J. Math. Mech. (to appear).

  2. Bochner, S., & W. T. Martin, Several Complex Variables. Princeton. Princeton Univ. Press 1948.

    Google Scholar 

  3. Focke, J., Asymptotische Entwicklungen Mittels der Methode der Stationären Phase. Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig 101, 1–48 (1954).

    Google Scholar 

  4. Friedrichs, K. O., Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7, 345–393 (1954).

    Google Scholar 

  5. Gantmacher, F. R., The Theory of Matrices, vol. 1. New York: Chelsea Publishing Co. 1959.

    Google Scholar 

  6. Grusin, V. V., On Sommerfeld-type conditions for a certain class of partial differential equations. Mat. Sb. (N. S.) 61 (103), 147–174 (1963). [A. M. S. Transl., Ser. 2, 51, 82–112 (1966).]

    Google Scholar 

  7. Hörmander, L., Linear Partial Differential Operators. Berlin-Göttingen-Heidelberg: Springer 1963.

    Google Scholar 

  8. Lighthill, M. J., Studies on magneto-hydrodynamic waves and other anisotropic wave motions. Philos. Trans. Roy. Soc. London Ser. A., 252, 397–470 (1960).

    Google Scholar 

  9. Littman, W., Fourier transforms of surface-carried measurer and differentiability of surface averages. Bull. Amer. Math. Soc. 69, 766–770 (1963).

    Google Scholar 

  10. Littman, W., Decay at infinity of solutions of partial differential equations with constant coefficients. Trans. Amer. Math. Soc. 123, 449–459 (1966).

    Google Scholar 

  11. Schwartz, L., Théorie des distributions, vol. I. Paris: Hermann 1950.

    Google Scholar 

  12. Vainberg, B. R., Asymptotic representation of fundamental solutions of hypoelliptic equations. Soviet Math. Dokl. 3, 914–916 (1962).

    Google Scholar 

  13. Vainberg, B. R., Hypoelliptic equations in the whole space and the principle of limiting absorption. Soviet Math. Dokl. 5, 321–324 (1964).

    Google Scholar 

  14. Veblen, O., Invariants of Quadratic Differential Forms. Cambridge: Cambridge Univ. Press 1927.

    Google Scholar 

  15. Wilcox, C. H., Wave operators and asymptotic solutions of wave propagation problems of classical physics. Arch. Rational Mech. Anal. 22, 37–78 (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by J. Serrin

Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wilcox, C.H. Steady-state wave propagation in homogeneous anisotropic media. Arch. Rational Mech. Anal. 25, 201–242 (1967). https://doi.org/10.1007/BF00251589

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00251589

Keywords

Navigation