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Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 291-304. doi: 10.3934/nhm.2024013
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Research article

Inverse problem of determining diffusion matrix between different structures for time fractional diffusion equation

  • 1.
    School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
  • 2.
    Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
  • Received: 20 December 2023 Revised: 12 March 2024 Accepted: 17 March 2024 Published: 21 March 2024

  • In this paper we consider some inverse problems of determining the diffusion matrix between different structures for the time fractional diffusion equation featuring a Caputo derivative. We first study an inverse problem of determining the diffusion matrix in the period structure using data from the corresponding homogenized equation, then we investigate an inverse problem of determining the diffusion matrix in the homogenized equation using data from the corresponding period structure of the oscillating equation. Finally, we establish the stability and uniqueness for the first inverse problem, and the asymptotic stability for the second inverse problem.

    Citation: Feiyang Peng, Yanbin Tang. Inverse problem of determining diffusion matrix between different structures for time fractional diffusion equation[J]. Networks and Heterogeneous Media, 2024, 19(1): 291-304. doi: 10.3934/nhm.2024013

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  • In this paper we consider some inverse problems of determining the diffusion matrix between different structures for the time fractional diffusion equation featuring a Caputo derivative. We first study an inverse problem of determining the diffusion matrix in the period structure using data from the corresponding homogenized equation, then we investigate an inverse problem of determining the diffusion matrix in the homogenized equation using data from the corresponding period structure of the oscillating equation. Finally, we establish the stability and uniqueness for the first inverse problem, and the asymptotic stability for the second inverse problem.




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