Uniqueness of the solution to inverse obstacle scattering with non-over-determined data. (August 2016)

• Record Type: Journal Article
• Authors: Ramm, Alexander G.
• Is Part Of: Applied mathematics letters. Volume 58(2016:Aug.)
• Page Start: 81
• Page End: 86
• Publication Date: 2016-08
• Subjects: Scattering theory -- Obstacle scattering -- Uniqueness theorem -- Non-over-determined scattering data; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.02.006
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: It is proved that the scattering amplitude A ( β, α 0, k 0 ), known for all β ∈ S 2, where S 2 is the unit sphere in R 3, α 0 ∈ S 2 is fixed, k 0 > 0 is fixed, determines the surface S of the obstacle and the boundary condition on S uniquely. The boundary condition on S is either the Dirichlet, or Neumann, or the impedance one. The uniqueness theorems for the solution of inverse scattering problems with non-over-determined data were not known for many decades. Such a theorem is proved in this paper for inverse scattering by obstacles for the first time.