scholarly journals Variational Regularization For The Inverse Problem of a Nonlinear Time-Fractional Diffusion Equations

2022 ◽  
Vol 43 (0) ◽  
pp. 1-12
Author(s):  
LIU Mian ◽  
◽  
◽  
CHENG Hao ◽  
SHI Chengxin
Keyword(s):  
Inverse Problem ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Variational Regularization

scholarly journals Identification of points sources via time fractional diffusion equation

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6189-6201 ◽  
Author(s):  
A. Ghanmi ◽  
R. Mdimagh ◽  
I.B. Saad
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Stability Result ◽  
Fractional Diffusion ◽  
Cauchy Data ◽  
Diffusion Equations ◽  
Lipschitz Stability ◽  
Single Measurement ◽  
Fractional Diffusion Equations ◽  
Time Fractional Diffusion Equation

This article investigates the source identification in the fractional diffusion equations, by performing a single measurement of the Cauchy data on the accessible boundary. The main results of this work consist in giving an identifiability result and establishing a local Lipschitz stability result. To solve the inverse problem of identifying fractional sources from such observations, a non-iterative algebraical method based on the Reciprocity Gap functional is proposed.

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