Journal
IMA JOURNAL OF APPLIED MATHEMATICS
Volume 82, Issue 3, Pages 579-600Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imamat/hxx004
Keywords
fractional diffusion; inverse potential problem; monotonicity; contraction; regularization; iterative algorithm
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Funding
- AFOSR MURI center for Material Failure Prediction through peridynamics
- ARO MURI Grant [W911NF-15-1-0562]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1319052] Funding Source: National Science Foundation
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In this article, we consider an inverse problem of recovering the potential term in a 1D time-fractional diffusion equation from the overdetermined final time data. We introduce a reconstruction operator and show its contractivity and monotonicity, which give the unique determination and an efficient algorithm. Further, for noisy data, we propose a regularized iterative algorithm based on mollification and derive error estimates for the approximation. Extensive numerical experiments for both smooth and nonsmooth potential data are provided to illustrate the efficiency and stability of the algorithm, and to verify the convergence theory.
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