Identification of Source Term for the Time-Fractional Diffusion-Wave Equation by Fractional Tikhonov Method
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-10-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/7/10/934 |
| Summary: | 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 <i>a priori</i> and <i>a posteriori</i> parameter choice rules and analyze them. |
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| ISSN: | 2227-7390 |