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November 2005 The Herglotz wave function, the Vekua transform and the enclosure method
Masaru Ikehata
Hiroshima Math. J. 35(3): 485-506 (November 2005). DOI: 10.32917/hmj/1150998324


This paper gives applications of the enclosure method introduced by the author to typical inverse obstacle and crack scattering problems in two dimensions. Explicit extraction formulae of the convex hull of unknown polygonal sound-hard obstacles and piecewise linear cracks from the far field pattern of the scattered field at a fixed wave number and at most two incident directions are given. The main new points of this paper are: a combination of the enclosure method and the Herglotz wave function; explicit construction of the density in the Herglotz wave function by using the idea of the Vekua transform. By virtue of the construction, one can avoid any restriction on the wave number in the extraction formulae. An attempt for the case when the far field pattern is given on limited angles is also given.


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Masaru Ikehata. "The Herglotz wave function, the Vekua transform and the enclosure method." Hiroshima Math. J. 35 (3) 485 - 506, November 2005.


Published: November 2005
First available in Project Euclid: 22 June 2006

zbMATH: 1106.35134
MathSciNet: MR2210721
Digital Object Identifier: 10.32917/hmj/1150998324

Primary: 35R30
Secondary: 35J05

Rights: Copyright © 2005 Hiroshima University, Mathematics Program


Vol.35 • No. 3 • November 2005
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