ITM Web Conf.
Volume 20, 2018International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|Number of page(s)||9|
|Section||Numerical and Applied Analysis|
|Published online||12 October 2018|
A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source
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
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
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