Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Scattering relations for point-generated dyadic fields in two-dimensional linear elasticity

Authors: C. Athanasiadis, V. Sevroglou and I. G. Stratis
Journal: Quart. Appl. Math. 64 (2006), 695-710
MSC (2000): Primary 74J20; Secondary 74B05
DOI: https://doi.org/10.1090/S0033-569X-06-01041-0
Published electronically: October 31, 2006
MathSciNet review: 2284466
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Abstract: The problem of scattering of elastic waves by a bounded obstacle in two-dimensional linear elasticity is considered. The scattering problems are presented in a dyadic form. An incident dyadic field generated by a point source is disturbed by a rigid body, a cavity, or a penetrable obstacle. General scattering theorems are proved, relating the far-field patterns due to scattering of waves from a point source set up in either of two different locations. The most general reciprocity theorem is established, and mixed scattering relations are also proved. Finally, a relation between the incident and the scattered wave which refers to the mechanism of energy transfer of the scatterer, the so-called optical theorem, is established.

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C. Athanasiadis
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis, GR 157 84 Athens, Greece
Email: cathan@math.uoa.gr

V. Sevroglou
Affiliation: Department of Mathematics, University of Ioannina, GR 45110 Ioannina, Greece
Email: bsevro@cc.uoi.gr

I. G. Stratis
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis, GR 157 84 Athens, Greece
Email: istratis@math.uoa.gr

DOI: https://doi.org/10.1090/S0033-569X-06-01041-0
Keywords: Dyadic scattering, point sources, scattering relations
Received by editor(s): January 19, 2006
Published electronically: October 31, 2006
Additional Notes: The authors acknowledge partial financial support from EPEAEK II (“Pythagoras II” research fellowships, project title “Mathematical Analysis of Wave Propagation in Chiral Electromagnetic and Elastic Media”, University of Athens).
Article copyright: © Copyright 2006 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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