Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

The Atkinson-Wilcox expansion theorem for elastic waves


Author: George Dassios
Journal: Quart. Appl. Math. 46 (1988), 285-299
MSC: Primary 73D25
DOI: https://doi.org/10.1090/qam/950603
MathSciNet review: 950603
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Abstract: Consider the problem of scattering of an elastic wave by a three-dimensional bounded and smooth body. In the region exterior to a sphere that includes the scatterer, any solution of Navier's equation that satisfies the Kupradze's radiation condition has a uniformly and absolutely convergent expansion in inverse powers of the radial distance from the center of the sphere. Moreover, the coefficients of the expansion can recurrently be evaluated from the knowledge of the leading coefficient, known as radiation pattern. Therefore, a one-to-one correspondence between the scattered fields and the corresponding radiation patterns is established. The acoustic and electromagnetic cases are recovered as special cases.


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DOI: https://doi.org/10.1090/qam/950603
Article copyright: © Copyright 1988 American Mathematical Society

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