Opuscula Math. 35, no. 2 (2015), 143-159

Opuscula Mathematica

On small vibrations of a damped Stieltjes string

Olga Boyko
Vyacheslav Pivovarchik

Abstract. Inverse problem of recovering masses, coefficients of damping and lengths of the intervals between the masses using two spectra of boundary value problems and the total length of the Stieltjes string (an elastic thread bearing point masses) is considered. For the case of point-wise damping at the first counting from the right end mass the problem of recovering the masses, the damping coefficient and the lengths of the subintervals by one spectrum and the total length of the string is solved.

Keywords: damping, Dirichlet boundary condition, point mass, Hermite-Biehler polynomial, continued fraction, eigenvalues.

Mathematics Subject Classification: 35Q99, 39A99.

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  • Olga Boyko
  • South-Ukrainian National Pedagogical University, Staroportofrankovskaya Str. 26, 65020, Odessa, Ukraine
  • Vyacheslav Pivovarchik
  • South-Ukrainian National Pedagogical University, Staroportofrankovskaya Str. 26, 65020, Odessa, Ukraine
  • Communicated by Alexander Gomilko.
  • Received: 2013-10-19.
  • Accepted: 2014-06-18.
  • Published online: 2014-11-18.
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Cite this article as:
Olga Boyko, Vyacheslav Pivovarchik, On small vibrations of a damped Stieltjes string, Opuscula Math. 35, no. 2 (2015), 143-159, http://dx.doi.org/10.7494/OpMath.2015.35.2.143

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