Initial inverse problem in heat equation with Bessel operator

Khalid Masood; Salim Messaoudi; F. D. Zaman

doi:10.1016/S0017-9310(02)00019-4

Initial inverse problem in heat equation with Bessel operator

Khalid Masood^*, Salim Messaoudi, F. D. Zaman

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

27 Scopus citations

Abstract

We investigate the inverse problem involving recovery of initial temperature from the information of final temperature profile in a disc. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. We consider the usual heat equation and the hyperbolic heat equation with Bessel operator. An integral representation for the problem is found, from which a formula for initial temperature is derived using Picard's criterion and the singular system of the associated operators.

Original language	English
Pages (from-to)	2959-2965
Number of pages	7
Journal	International Journal of Heat and Mass Transfer
Volume	45
Issue number	14
DOIs	https://doi.org/10.1016/S0017-9310(02)00019-4
State	Published - 13 May 2002

Bibliographical note

Funding Information:
The authors wish to acknowledge the support provided by the King Fahd University of Petroleum and Minerals.

ASJC Scopus subject areas

Condensed Matter Physics
Mechanical Engineering
Fluid Flow and Transfer Processes

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10.1016/S0017-9310(02)00019-4

Cite this

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title = "Initial inverse problem in heat equation with Bessel operator",

abstract = "We investigate the inverse problem involving recovery of initial temperature from the information of final temperature profile in a disc. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. We consider the usual heat equation and the hyperbolic heat equation with Bessel operator. An integral representation for the problem is found, from which a formula for initial temperature is derived using Picard's criterion and the singular system of the associated operators.",

author = "Khalid Masood and Salim Messaoudi and Zaman, \{F. D.\}",

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AU - Masood, Khalid

AU - Messaoudi, Salim

AU - Zaman, F. D.

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

PY - 2002/5/13

Y1 - 2002/5/13

N2 - We investigate the inverse problem involving recovery of initial temperature from the information of final temperature profile in a disc. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. We consider the usual heat equation and the hyperbolic heat equation with Bessel operator. An integral representation for the problem is found, from which a formula for initial temperature is derived using Picard's criterion and the singular system of the associated operators.

AB - We investigate the inverse problem involving recovery of initial temperature from the information of final temperature profile in a disc. This inverse problem arises when experimental measurements are taken at any given time, and it is desired to calculate the initial profile. We consider the usual heat equation and the hyperbolic heat equation with Bessel operator. An integral representation for the problem is found, from which a formula for initial temperature is derived using Picard's criterion and the singular system of the associated operators.

UR - https://www.scopus.com/pages/publications/0037071506

U2 - 10.1016/S0017-9310(02)00019-4

DO - 10.1016/S0017-9310(02)00019-4

M3 - Article

AN - SCOPUS:0037071506

SN - 0017-9310

VL - 45

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EP - 2965

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

IS - 14

ER -

Initial inverse problem in heat equation with Bessel operator

Abstract

Bibliographical note

ASJC Scopus subject areas

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