Journal of Operator Theory

Volume 38, Issue 2, Fall 1997 pp. 243-263.

Inverse problem for a smooth string with damping at one end

Authors: Vyacheslav N. Pivovarchik
Author institution:Department of Higher Mathematics, Odessa Academy of Civil Engineering and Architecture, Didrihson str. 4, 270029, Odessa, UKRAINE

Summary: Direct and inverse spectral problems for a smooth string with massive end (with concentrated mass at the end) moving with damping is considered. By means of Liouville transformation the problem has been reduced to the Sturm-Liouville equation with boundary conditions depending on the spectral parameter. So the V.A. Marchenko formalism proves to be a powerful tool of investigation. It is shown in this paper that the spectrum of vibrations and the length of the string are sufficient for finding all the parameters of the problem.

Keywords: Inverse problem, Sturm-Liouville equation.

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