Identifying source term in the subdiffusion equation with L 2-TV regularization

We consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this problem. Based on these results, we consider an inverse problem of identification of a space-dependent coefficient of a linear reaction term. We prove the uniqueness and local existence and stability of the solution to this problem.

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Finite element approximation of source term identification with TV-regularization

Inverse Problems ◽

10.1088/1361-6420/ab3478 ◽

2019 ◽

Vol 35 (12) ◽

pp. 124004 ◽

Cited By ~ 2

Author(s):

Michael Hinze ◽

Tran Nhan Tam Quyen

Keyword(s):

Finite Element ◽

Source Term ◽

Finite Element Approximation ◽

Element Approximation ◽

Tv Regularization ◽

Term Identification

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Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2009.02.013 ◽

2009 ◽

Vol 231 (1) ◽

pp. 160-176 ◽

Cited By ~ 155

Author(s):

F. Liu ◽

C. Yang ◽

K. Burrage

Keyword(s):

Numerical Method ◽

Source Term ◽

Nonlinear Source ◽

Analytical Technique ◽

Subdiffusion Equation

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INVERSE PROBLEMS FOR A GENERALIZED SUBDIFFUSION EQUATION WITH FINAL OVERDETERMINATION

Mathematical Modelling and Analysis ◽

10.3846/10.3846/mma.2019.016 ◽

2019 ◽

Vol 24 (2) ◽

pp. 236-262 ◽

Cited By ~ 5

Author(s):

Jaan Janno ◽

Nataliia Kinash

Keyword(s):

Inverse Problem ◽

Inverse Problems ◽

Source Term ◽

Local Existence ◽

Reaction Term ◽

Dependent Component ◽

Linear Reaction ◽

Existence And Stability ◽

Subdiffusion Equation ◽

Stability Of The Solution

We consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this problem. Based on these results, we consider an inverse problem of identification of a space-dependent coefficient of a linear reaction term. We prove the uniqueness and local existence and stability of the solution to this problem.

Download Full-text