Degree Type

Dissertation

Date of Award

2008

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Paul E. Sacks

Second Advisor

Fritz Keinert

Third Advisor

Justin Peters

Abstract

An eigenvalue problem for a Sturm-Liouville differential operator containing a parameter function and being studied on a given domain is a model for the infinitesimal, vertical vibration of a string of negligible mass, with the ends subject to various constraints. The parameter function of the Sturm-Liouville operator encodes information about the string (its density), and the eigenvalues of the same operator are the squares of the natural frequencies of oscillation of the string. In an inverse Sturm-Liouville problem one has knowledge about the spectral data of the operator and tries to recover the parameter function of the same operator. This thesis deals with the recovery of the parameter function of a Sturm-Liouville operator from knowledge of three sets of eigenvalues. The recovery is achieved theoretically and numerically in two different situations: (a) when the three sets correspond respectively to the vibration of the whole string fixed only at the end points, and the vibrations of each individual piece obtained by fixing the string at an interior node; (b) when the three sets correspond respectively to the vibration of the whole string fixed only at the end points, and the vibrations of each individual piece obtained by attaching the string at an interior node to a spring with a known stiffness constant. Situations when existence or uniqueness of the parameter function is lost are also presented.

DOI

https://doi.org/10.31274/rtd-180813-16905

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Mihaela Cristina Drignei

Language

en

Proquest ID

AAI3316216

OCLC Number

271223854

ISBN

9780549688532

File Format

application/pdf

File Size

167 pages

Included in

Mathematics Commons

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