On a Reconstruction of a Solely Time-Dependent Source in a Time-Fractional Diffusion Equation with Non-smooth Solutions

2021 ◽  
Vol 90 (1) ◽  
Author(s):  
A. S. Hendy ◽  
K. Van Bockstal
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Time Dependent ◽  
Smooth Solutions ◽  
Time Fractional Diffusion Equation

Recovering a time-dependent potential function in a multi-term time fractional diffusion equation by using a nonlinear condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Su Zhen Jiang ◽  
Yu Jiang Wu
Keyword(s):  
Diffusion Equation ◽  
Potential Function ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Time Dependent ◽  
Potential Term ◽  
Nonlinear Condition ◽  
Dependent Potential ◽  
Time Fractional Diffusion Equation ◽  
The Fixed Point Theorem

AbstractIn the present paper, we devote our effort to a nonlinear inverse problem for recovering a time-dependent potential term in a multi-term time fractional diffusion equation from an additional measurement in the form of an integral over the space domain. First we study the existence, uniqueness, regularity and stability of the solution for the direct problem by using the fixed point theorem. And we obtain the uniqueness of the inverse time-dependent potential term problem. Numerically, we use the Levenberg–Marquardt method to find the approximate potential function. Four different examples are presented to show the feasibility and efficiency of the proposed method.

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