Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] J. F. Ahner and R. E. Kleinman, The exterior Neumann problem for the Helmholtz equation, Arch. Rational Mech. Anal. 52 (1973), 26–43. MR 0336044, https://doi.org/10.1007/BF00249090
  • [2] George Bachman and Lawrence Narici, Functional analysis, Academic Press, New York-London, 1966. MR 0217549
  • [3] L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964. MR 0213845
  • [4] Oliver Dimon Kellogg, Foundations of potential theory, Reprint from the first edition of 1929. Die Grundlehren der Mathematischen Wissenschaften, Band 31, Springer-Verlag, Berlin-New York, 1967. MR 0222317
  • [5] V. D. Kupradze, Potential methods in the theory of elasticity, Translated from the Russian by H. Gutfreund. Translation edited by I. Meroz, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., New York, 1965. MR 0223128
  • [6] S. L. Sobolev, Partial differential equations of mathematical physics, Pergamon Press, Oxford, 1964

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73.45

Retrieve articles in all journals with MSC: 73.45

Additional Information

DOI: https://doi.org/10.1090/qam/449124
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society