dc.contributor.author Arbuzov, E. V. dc.contributor.author Bukhgeim, A. A. dc.contributor.author Bukhgeym, Alexander L. dc.date.accessioned 2013-07-23T16:27:59Z dc.date.available 2013-07-23T16:27:59Z dc.date.issued 2008 dc.identifier.citation Arbuzov, E. V.; Bukhgeim, A. A.; Bukhgeim, A. L. 2008. The Carleman formula and recovering the refractive index of the two-dimensional Helmholtz equation. Proceedings of the International Conference on Mathematical Methods in Geophysics “MMG-2008". Akademgorodok, Novosibirsk, Russia, October 13-15, 2008 : 1-6. en_US dc.identifier.uri http://hdl.handle.net/10057/6025 dc.description.abstract We consider the Cauchy problem for the Helmholtz equation with given bounded refrac- en_US tive index in an arbitrary planar domain with Cauchy data only on part of the boundary of the domain. We derive a Carleman-type formula for a solution to this problem. From another side we obtain the inversion formula for smooth unknown refractive index using the Cauchy date set on the boundary. Based of this inversion formula we numerically reconstruct the refractive index on the unit disk. dc.language.iso en_US en_US dc.relation.ispartofseries International Conference on Mathematical Methods in Geophysics;2008 dc.title The Carleman formula and recovering the refractive index of the two-dimensional Helmholtz equation en_US dc.type Conference paper en_US
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