| Issue |
ITM Web Conf.
Volume 20, 2018
International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|
|
|---|---|---|
| Article Number | 02007 | |
| Number of page(s) | 9 | |
| Section | Numerical and Applied Analysis | |
| DOI | https://doi.org/10.1051/itmconf/20182002007 | |
| Published online | 12 October 2018 | |
A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source
1
Faculty of Basic Science, Posts and Telecommunications, Institute of Technology, Ho Chi Minh City, Vietnam
2
Faculty of Mathematics and Computer Science, University of Science, Vietnam National University
(VNU-HCMC), Ho Chi Minh City, Vietnam
3
Faculty of Fundamental Science, Nguyen Hue University, Dong Nai, Viet Nam
4
Department of Applied Mathematics, Faculty of Applied Science, University of Technology (VNUHCM), Ho Chi Minh City, Viet Nam
5
Department of Mathematics, Faculty of Science, Nong Lam University, Ho Chi Minh City, Viet Nam
*
e-mail: lvcamhoan@gmail.com
**
e-mail: binhlucquan@gmail.com
***
e-mail: tranbaongoc@hcmuaf.edu.vn
In the present paper, we consider a time-fractional inverse diffusion problem with an in-homogeneous source, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We propose a regularization method to solve it based on the solution given by the Fourier method.
Key words: Ill-posed problem / time fractional diffusion equation / regularization / regularized truncation method
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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