Well-posedness of the Goursat problem and stability for point source inverse backscattering. (8th November 2017)

• Record Type: Journal Article
• Authors: Blåsten, Eemeli
• Is Part Of: Inverse problems. Volume 33:Number 12(2017:Dec.)
• Publication Date: 2017-11-08
• Subjects: inverse backscattering -- point source -- Goursat problem -- stability; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa941f
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We show logarithmic stability for the point source inverse backscattering problem under the assumption of angularly controlled potentials. Radial symmetry implies Hölder stability. Importantly, we also show that the point source equation is well-posed and also that the associated characteristic initial value problem, or Goursat problem, is well-posed. These latter results are difficult to find in the literature in the form required by the stability proof.