Please use this identifier to cite or link to this item: dspace.pdpu.edu.ua/jspui/handle/123456789/5320
Title: Direct and inverse problems for a damped string
Authors: Пивоварчик, В’ячеслав Миколайович
Пивоварчик, Вячеслав Николаевич
Pyvovarchyk, Viacheslav Mykolayovуch
Keywords: Inverse problem
Sturm-Liouville equation
damped string vibrations
operator pencil
Issue Date: 1999
Publisher: American Mathematical Society
Citation: Pivovarchik V. Direct and inverse problems for a damped string / V. Pivovarchik // Journal of Operator Theory. – 1999. – № 42. – P. 189-220.
Abstract: In this paper small transverse vibrations of a string of inhomogeneous stiffness in a damping medium with the left end fixed and the right end equipped with a concentrated mass are considered. By means of the Liouville transformation the corresponding differential equation is reduced to a Sturm–Liouville problem with parameter-dependent boundary conditions and parameter-dependent potential. This problem is considered as a spectral problem for the corresponding quadratic operator pencil. The inverse problem, i.e. the determination of the potential and the boundary conditions by the given spectrum and length of the string, is solved for weakly damped strings (having no purely imaginary eigenvalues). Uniqueness of the solution in an appropriate class is proved.
URI: dspace.pdpu.edu.ua/jspui/handle/123456789/5320
Appears in Collections:Кафедра вищої математики і статистики

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