Wave phenomena in inhomogeneous media
Author:
Paul Filippi
Journal:
Quart. Appl. Math. 33 (1976), 337-350
MSC:
Primary 49G10; Secondary 65P05
DOI:
https://doi.org/10.1090/qam/458305
MathSciNet review:
458305
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Abstract: The difference between the fundamental solutions of differential equations governing the same physical phenomenon in two different physical media is investigated. A stationary expression of this difference is established, leading to a Ritz-Galerkin procedure. The Ritz-Galerkin system is solved analytically, providing a representing series for the difference of the two fundamental solutions as a functional of either one or the other of these functions. The convergence of the series is a consequence of its construction itself. Physical examples are considered which show that the convergence rate can be partially controlled.
G. Canevet, G. P. Extremet and M. Jessel, Propagation du son dans un dioptre flou, Acustica 26, 102–107(1972); U. Frisch, Propagation d’ondes et rayons en milieu aleatoire, Rev. Cethedec, No. 15, 3d trimester, 1968; D. S. Saxon, Formulation of high energy potential scattering problems, Phys. Rev. 107, 871–876(1957); S. R. S. Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients, Comm. Pure Appl. Math. 20, 431–455(1967); E. J. Kanellopoulos, T. V. Kanellopoulos and K. Wildemuth, Comm. Math. Phys. 24, 225–242 (1972)
- Stefan Bergman, The kernel function and conformal mapping, Second, revised edition, American Mathematical Society, Providence, R.I., 1970. Mathematical Surveys, No. V. MR 0507701
A. W. Leissa, Vibration of plates, NASA SP-160, 1969
P. Filippi and H. Saadat, Vibration d’une plaque mince couplee avec un fluide, Acustica 26, 315–322 (1972); H. Saadat, Etude des vibrations d’une plaque mince couplee avec un fluide, These d’Etat, Marseille, 1972
- Leonid M. Brekhovskikh, Waves in layered media, Applied Mathematics and Mechanics, Vol. 6, Academic Press, New York-London, 1960. Translated from the Russian by David Lieberman; translation edited by Robert T. Beyer. MR 0112392
G. Canevet, G. P. Extremet and M. Jessel, Propagation du son dans un dioptre flou, Acustica 26, 102–107(1972); U. Frisch, Propagation d’ondes et rayons en milieu aleatoire, Rev. Cethedec, No. 15, 3d trimester, 1968; D. S. Saxon, Formulation of high energy potential scattering problems, Phys. Rev. 107, 871–876(1957); S. R. S. Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients, Comm. Pure Appl. Math. 20, 431–455(1967); E. J. Kanellopoulos, T. V. Kanellopoulos and K. Wildemuth, Comm. Math. Phys. 24, 225–242 (1972)
S. Bergmann, The kernel function and conformal mapping, Amer. Math. Soc., Providence, 1970
A. W. Leissa, Vibration of plates, NASA SP-160, 1969
P. Filippi and H. Saadat, Vibration d’une plaque mince couplee avec un fluide, Acustica 26, 315–322 (1972); H. Saadat, Etude des vibrations d’une plaque mince couplee avec un fluide, These d’Etat, Marseille, 1972
L. M. Brekhovskikh, Waves in layered media, Academic Press, New York, 1960
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Article copyright:
© Copyright 1976
American Mathematical Society
