A Neumann series representation for solutions to boundary-value problems in dynamic elasticity
Authors:
John F. Ahner and George C. Hsiao
Journal:
Quart. Appl. Math. 33 (1975), 73-80
MSC:
Primary 73.45
DOI:
https://doi.org/10.1090/qam/449124
MathSciNet review:
449124
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Abstract: A regularized integral equation formulation for two exterior fundamental boundary-value problems in elastodynamics is presented. In either case, the displacement vector is assumed to be harmonic in time with a small frequency. It is shown that the solution can be expressed as a Neumann series in terms of the prescribed function; moreover, a sufficient condition for the convergence of the series is established.
- J. F. Ahner and R. E. Kleinman, The exterior Neumann problem for the Helmholtz equation, Arch. Rational Mech. Anal. 52 (1973), 26–43. MR 336044, DOI https://doi.org/10.1007/BF00249090
- George Bachman and Lawrence Narici, Functional analysis, Academic Press, New York-London, 1966. MR 0217549
- L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964. Translated from the Russian by D. E. Brown; Edited by A. P. Robertson. MR 0213845
- Oliver Dimon Kellogg, Foundations of potential theory, Die Grundlehren der Mathematischen Wissenschaften, Band 31, Springer-Verlag, Berlin-New York, 1967. Reprint from the first edition of 1929. MR 0222317
- V. D. Kupradze, Potential methods in the theory of elasticity, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., New York, 1965. Translated from the Russian by H. Gutfreund; Translation edited by I. Meroz. MR 0223128
S. L. Sobolev, Partial differential equations of mathematical physics, Pergamon Press, Oxford, 1964
J. F. Ahner and R. E. Kleinman, The exterior Neumann problem for the Helmholtz equation, Arch. Rat. Mech. Anal. 52, 26–43 (1973)
G. Bachman and L. Narici, Functional analysis, Academic Press, New York, 1966, p. 271
L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, Macmillan, New York, 1964, p. 173
O. D. Kellogg, Foundations of potential theory, Springer-Verlag, Berlin, 1929, p. 217
V. D. Kupradze, Potential methods in the theory of elasticity, Israel Program for Scientific Translations, Jerusalem, 1965
S. L. Sobolev, Partial differential equations of mathematical physics, Pergamon Press, Oxford, 1964
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Article copyright:
© Copyright 1975
American Mathematical Society