Inverse source problem for a diffusion equation involving the fractional spectral Laplacian

In this paper, we consider an inverse problem related to a fractional diffusion equation. The model problem is governed by a nonlinear partial differential equation involving the fractional spectral Laplacian. This study is focused on the reconstruction of an unknown source term from a partial inter...

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Vydáno v:Mathematical methods in the applied sciences Ročník 44; číslo 1; s. 917 - 936
Hlavní autoři: BenSalah, Mohamed, Hassine, Maatoug
Médium: Journal Article
Jazyk:angličtina
Vydáno: Freiburg Wiley Subscription Services, Inc 15.01.2021
Témata:
fractional diffusion equation
fractional spectral Laplacian
Inverse problems
inverse source problem
Iterative methods
minimization problem
Noise reduction
Nonlinear differential equations
nonlocal operator
numerical reconstruction algorithm
Optimization
Partial differential equations
Reconstruction
source term
ISSN:0170-4214, 1099-1476
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Shrnutí:In this paper, we consider an inverse problem related to a fractional diffusion equation. The model problem is governed by a nonlinear partial differential equation involving the fractional spectral Laplacian. This study is focused on the reconstruction of an unknown source term from a partial internal measured data. The considered ill‐posed inverse problem is formulated as a minimization one. The existence, uniqueness, and stability of the solution are discussed. Some theoretical results are established. The numerical reconstruction of the unknown source term is investigated using an iterative process. The proposed method involves a denoising procedure at each iteration step and provides a sequence of source term approximations converging in norm to the actual solution of the minimization problem. Some numerical results are presented to show the efficiency and the accuracy of the proposed approach.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6799