Solution to the interior transmission problem using nodes on a subinterval as input data. (June 2017)

• Record Type: Journal Article
• Authors: Yang, Chuan-Fu; Xu, Xiao-Chuan; Buterin, Sergey
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 20
• Page End: 29
• Publication Date: 2017-06
• Subjects: Interior transmission problem -- Inverse nodal problem -- Transmission eigenvalue; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.10.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: It is well known that a spherically symmetric wave speed problem in a bounded spherical region may be reduced, by means of Liouville transform, to the Sturm–Liouville problem B ( a ; q ) in [ 0, 1 ] . We prove that a twin dense subset of the nodal set in a subinterval ( ⊂ [ 0, 1 ] ) uniquely determines the potential q on the whole interval [ 0, 1 ] and the boundary parameter a . The method employed is to convert the inverse nodal problem into the inverse spectral problem with partial information given on the potential on a subinterval.