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The quasi‐reversibility method for a final value problem of the time‐fractional diffusion equation with inhomogeneous source
Author(s) -
Yang Fan,
Ren YuPeng,
Li XiaoXiao
Publication year - 2017
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.4705
Subject(s) - mathematics , regularization (linguistics) , a priori and a posteriori , inverse problem , heat equation , well posed problem , diffusion equation , convergence (economics) , thermal conduction , mathematical analysis , computer science , economy , economics , service (business) , philosophy , materials science , epistemology , artificial intelligence , economic growth , composite material
This paper is devoted to discuss a multidimensional backward heat conduction problem for time‐fractional diffusion equation with inhomogeneous source. This problem is ill‐posed. We use quasi‐reversibility regularization method to solve this inverse problem. Moreover, the convergence estimates between regularization solution and the exact solution are obtained under the a priori and the a posteriori choice rules. Finally, the numerical examples for one‐dimensional and two‐dimensional cases are presented to show that our method is feasible and effective.