tikhonov method
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Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 934
Author(s):  
Le Dinh Long ◽  
Nguyen Hoang Luc ◽  
Yong Zhou ◽  
and Can Nguyen

In this article, we consider an inverse problem to determine an unknown source term in a space-time-fractional diffusion equation. The inverse problems are often ill-posed. By an example, we show that this problem is NOT well-posed in the Hadamard sense, i.e., this problem does not satisfy the last condition-the solution’s behavior changes continuously with the input data. It leads to having a regularization model for this problem. We use the Tikhonov method to solve the problem. In the theoretical results, we also propose a priori and a posteriori parameter choice rules and analyze them.





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