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Recovering the source term for parabolic equation with nonlocal integral condition
Author(s) -
Duc Phuong Nguyen,
Baleanu Dumitru,
Thanh Phong Tran,
Dinh Long Le
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7331
Subject(s) - tikhonov regularization , mathematics , a priori and a posteriori , regularization (linguistics) , well posed problem , term (time) , mathematical analysis , heat equation , inverse problem , computer science , philosophy , physics , epistemology , quantum mechanics , artificial intelligence
The main purpose of this article is to present a Tikhonov method to construct the source function f ( x ) of the parabolic diffusion equation. This problem is well known to be severely ill‐posed. Therefore, regularization is required. The error estimates between the sought solution and the regularized solution are obtained under an a priori parameter choice rule and an a posteriori parameter choice rule, respectively. One numerical test illustrates that the proposed method is feasible and effective.