Identification of a wave equation generated by a string∗. (8th August 2014)

• Record Type: Journal Article
• Authors: Boumenir, Amin
• Is Part Of: ESAIM. Volume 20:Number 4(2014:Oct.)
• Page Start: 1203
• Page End: 1213
• Publication Date: 2014-08-08
• Subjects: Inverse spectral methods; Krein string; Gelfand-Levitan theory; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2014012
• Languages: English
• ISSNs: 1292-8119

Abstract

Abstract : We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein's inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.