Identification and regularization for unknown source for a time-fractional diffusion equation

Nguyen Huy Tuan; Mokhtar Kirane; Luu Vu Cam Hoan; Le Dinh Long

doi:10.1016/j.camwa.2016.10.002

Identification and regularization for unknown source for a time-fractional diffusion equation

Nguyen Huy Tuan, Mokhtar Kirane, Luu Vu Cam Hoan, Le Dinh Long

Mathematics

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

21 Scopus citations

Abstract

In this paper, we consider the inverse problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate. Two numerical examples are presented to illustrate the validity and effectiveness of our method.

Original language	British English
Pages (from-to)	931-950
Number of pages	20
Journal	Computers and Mathematics with Applications
Volume	73
Issue number	6
DOIs	https://doi.org/10.1016/j.camwa.2016.10.002
State	Published - 15 Mar 2017

Keywords

Diffusion process
Fractional derivative
Inhomogeneous source
Inverse source problem
Regularization

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10.1016/j.camwa.2016.10.002

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title = "Identification and regularization for unknown source for a time-fractional diffusion equation",

abstract = "In this paper, we consider the inverse problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate. Two numerical examples are presented to illustrate the validity and effectiveness of our method.",

keywords = "Diffusion process, Fractional derivative, Inhomogeneous source, Inverse source problem, Regularization",

author = "Tuan, {Nguyen Huy} and Mokhtar Kirane and Hoan, {Luu Vu Cam} and Long, {Le Dinh}",

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AU - Tuan, Nguyen Huy

AU - Kirane, Mokhtar

AU - Hoan, Luu Vu Cam

AU - Long, Le Dinh

PY - 2017/3/15

Y1 - 2017/3/15

N2 - In this paper, we consider the inverse problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate. Two numerical examples are presented to illustrate the validity and effectiveness of our method.

AB - In this paper, we consider the inverse problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate. Two numerical examples are presented to illustrate the validity and effectiveness of our method.

KW - Diffusion process

KW - Fractional derivative

KW - Inhomogeneous source

KW - Inverse source problem

KW - Regularization

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EP - 950

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 6

ER -

Identification and regularization for unknown source for a time-fractional diffusion equation

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Keywords

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