Forward and Inverse Problems for a Finite Krein–Stieltjes String. Approximation of Constant Density by Point Masses

A dynamic inverse problem for a dynamical system that describes the propagation of waves in a Krein string is considered. The problem is reduced to an integral equation, and an important special case is considered where the string density is determined by a finite number of point masses distributed...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 252; no. 5; pp. 654 - 663
Main Authors Mikhaylov, A. S., Mikhaylov, V. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2021
Springer
Springer Nature B.V
Subjects
Approximation
Density
Dynamical systems
Integral equations
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Propagation velocity
Specific gravity
Strings
Wave propagation
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Summary:A dynamic inverse problem for a dynamical system that describes the propagation of waves in a Krein string is considered. The problem is reduced to an integral equation, and an important special case is considered where the string density is determined by a finite number of point masses distributed over the interval. An equation of Krein type, with the help of which the string density is restored, is derived. The approximation of constant density by point masses uniformly distributed over the interval and the effect of the appearance of a finite wave propagation velocity in the dynamical system are also studied.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05188-7