scholarly journals Time-fractional diffusion equation with dynamical boundary condition

2016 ◽  
pp. 151-178 ◽  
Author(s):  
Mykola Krasnoschok
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Dynamical Boundary Condition ◽  
Time Fractional Diffusion Equation

scholarly journals Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
L. L. Sun ◽  
X. B. Yan
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Source Function ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Nonhomogeneous Boundary Condition ◽  
Nonhomogeneous Boundary ◽  
Time Fractional Diffusion Equation ◽  
Continuation Technique

This paper is devoted to identify a space-dependent source function in a multiterm time-fractional diffusion equation with nonhomogeneous boundary condition from a part of noisy boundary data. The well-posedness of a weak solution for the corresponding direct problem is proved by the variational method. We firstly investigate the uniqueness of an inverse initial problem by the analytic continuation technique and the Laplace transformation. Then, the uniqueness of the inverse source problem is derived by employing the fractional Duhamel principle. The inverse problem is solved by the Levenberg-Marquardt regularization method, and an approximate source function is found. Numerical examples are provided to show the effectiveness of the proposed method in one- and two-dimensional cases.

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