Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source-Reference-Cited by-同舟云学术

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

Published:2020-04-01 Issue:2 Volume:28 Page:211-235
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:
Short-container-title:

Author:

Ngoc Tran Bao¹,Tuan Nguyen Huy²,Kirane Mokhtar³

Affiliation:

1. Institute of Research and Development, Duy Tan University, Da Nang550000; and Department of Mathematics and Computer Science, VNUHCM-University of Science, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam

2. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

3. Lasie, Faculté des Sciences et Technologies, Université de La Rochelle, Avenue M. Crépeau, La Rochelle, Cedex 17042, France

Abstract

AbstractIn 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.

Funder

National Foundation for Science and Technology Development

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2018-0040/pdf

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