The determination of the leading coefficient in the monotone potential Sturm-Liouville operator from boundary measurements

Hasanov A.

APPLIED MATHEMATICS AND COMPUTATION, vol.152, pp.141-162, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 152 Issue: 1
  • Publication Date: 2004
  • Doi Number: 10.1016/s0096-3003(03)00551-4
  • Page Numbers: pp.141-162


This paper deals with the problem of determining the leading coefficient k = k( (u')(2)) of the nonlinear (monotone potential) Sturm-Liouville operator Au = - (k ((u') (2)) u' (x))' + q(x)u(x), x epsilon (a,b). As an additional condition only two measured data at the boundary (x = a, x = b) are used. Solvability and linearization of the corresponding nonlinear direct problein are given. An existence of a quasi-solution of the inverse problem is obtained in a suitable compact class of admissible coefficients. In the second part of the paper an approximate analytical solution for the inverse problem is derived. The approach presented permits to analyze well-posed, as well as, all ill-posed situations for the inverse coefficient problem. Numerical examples corresponding to the Lill considered situations are presented. (C) 2003 Elsevier Inc. All rights reserved.