Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

Mokhtar Kirane; Salman A. Malik

doi:10.1016/j.amc.2011.05.084

Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

Mokhtar Kirane, Salman A. Malik

Mathematics

Université de La Rochelle

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

91 Scopus citations

Abstract

We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.

Original language	British English
Pages (from-to)	163-170
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	218
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2011.05.084
State	Published - 1 Sep 2011

Keywords

Biorthogonal system of functions
Fourier series
Fractional derivative
Heat equation
Integral equations
Inverse problem

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10.1016/j.amc.2011.05.084

Cite this

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title = "Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time",

abstract = "We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.",

keywords = "Biorthogonal system of functions, Fourier series, Fractional derivative, Heat equation, Integral equations, Inverse problem",

author = "Mokhtar Kirane and Malik, {Salman A.}",

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AU - Kirane, Mokhtar

AU - Malik, Salman A.

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N2 - We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.

AB - We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.

KW - Biorthogonal system of functions

KW - Fourier series

KW - Fractional derivative

KW - Heat equation

KW - Integral equations

KW - Inverse problem

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JO - Applied Mathematics and Computation

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ER -

Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

Abstract

Keywords

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