Investigation of the direct and inverse solutions for torsional waves propagating in a cylinder

F. D. Zaman; Khalid Masood

doi:10.1016/j.amc.2005.04.067

Investigation of the direct and inverse solutions for torsional waves propagating in a cylinder

F. D. Zaman^*
, Khalid Masood

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the direct and inverse problem associated with the torsional waves propagating in a cylinder. We analyse the usual wave equation as well as the damped wave equation and consider the problem of recovering the initial profile from the observations of the final profile. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. An integral representation for the problem is found, from which a formula for initial disturbance is derived using Picard's criterion and the singular system of the associated operators.

Original language	English
Pages (from-to)	1238-1245
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	173
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2005.04.067
State	Published - 15 Feb 2006

Bibliographical note

Funding Information:
The authors wish to acknowledge support provided by the King Fahd University of Petroleum and Minerals and the Hal Al-Batin Community College.

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2005.04.067

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abstract = "We investigate the direct and inverse problem associated with the torsional waves propagating in a cylinder. We analyse the usual wave equation as well as the damped wave equation and consider the problem of recovering the initial profile from the observations of the final profile. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. An integral representation for the problem is found, from which a formula for initial disturbance is derived using Picard's criterion and the singular system of the associated operators.",

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AU - Zaman, F. D.

AU - Masood, Khalid

N1 - Funding Information: The authors wish to acknowledge support provided by the King Fahd University of Petroleum and Minerals and the Hal Al-Batin Community College.

PY - 2006/2/15

Y1 - 2006/2/15

N2 - We investigate the direct and inverse problem associated with the torsional waves propagating in a cylinder. We analyse the usual wave equation as well as the damped wave equation and consider the problem of recovering the initial profile from the observations of the final profile. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. An integral representation for the problem is found, from which a formula for initial disturbance is derived using Picard's criterion and the singular system of the associated operators.

AB - We investigate the direct and inverse problem associated with the torsional waves propagating in a cylinder. We analyse the usual wave equation as well as the damped wave equation and consider the problem of recovering the initial profile from the observations of the final profile. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. An integral representation for the problem is found, from which a formula for initial disturbance is derived using Picard's criterion and the singular system of the associated operators.

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

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ER -

Investigation of the direct and inverse solutions for torsional waves propagating in a cylinder

Abstract

Bibliographical note

ASJC Scopus subject areas

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