Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source

Tran Bao Ngoc; Nguyen Huy Tuan; Mokhtar Kirane

doi:10.1515/jiip-2018-0040

Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source

Tran Bao Ngoc, Nguyen Huy Tuan, Mokhtar Kirane

Mathematics

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

4 Scopus citations

Abstract

In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.

Original language	British English
Pages (from-to)	211-235
Number of pages	25
Journal	Journal of Inverse and Ill-Posed Problems
Volume	28
Issue number	2
DOIs	https://doi.org/10.1515/jiip-2018-0040
State	Published - 1 Apr 2020

Keywords

Caputo's fractional derivatives
Fourier transform
Ill-posed
regularization method

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10.1515/jiip-2018-0040

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abstract = "In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.",

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AU - Tuan, Nguyen Huy

AU - Kirane, Mokhtar

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N2 - In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.

AB - In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.

KW - Caputo's fractional derivatives

KW - Fourier transform

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KW - regularization method

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ER -

Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source

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Keywords

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