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
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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.

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

  • [1] J. F. Ahner and R. E. Kleinman, The exterior Neumann problem for the Helmholtz equation, Arch. Rat. Mech. Anal. 52, 26-43 (1973) MR 0336044
  • [2] G. Bachman and L. Narici, Functional analysis, Academic Press, New York, 1966, p. 271 MR 0217549
  • [3] L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, Macmillan, New York, 1964, p. 173 MR 0213845
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DOI: https://doi.org/10.1090/qam/449124
Article copyright: © Copyright 1975 American Mathematical Society

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