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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical methods in the applied sciences Jg. 44; H. 1; S. 917 - 936
Hauptverfasser: BenSalah, Mohamed, Hassine, Maatoug
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Freiburg Wiley Subscription Services, Inc 15.01.2021
Schlagworte:
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
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6799