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Stability in Inverse Problem of Determining Two Parameters for the Moore-Gibson-Thompson Equation with Memory Terms

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Abstract

In this paper, the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity, which introduce a sort of delay in the dynamics, producing nonlocal effects in time. The Hölder stability of simultaneously determining the spatially varying viscosity coefficient and the source term is obtained by means of the key pointwise Carleman estimate for the Moore-Gibson-Thompson equation. For the sake of generality in mathematical tools, the analysis of this paper is discussed within the framework of Riemannian geometry.

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Author information

Authors and Affiliations

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Songren Fu, Liangbiao Chen & Ji-Feng Zhang

  2. School of Automation and Electrical Engineering, Zhongyuan University of Technology, Zhengzhou, 450007, China

    Ji-Feng Zhang

Authors
  1. Songren Fu
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  2. Liangbiao Chen
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  3. Ji-Feng Zhang
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Corresponding author

Correspondence to Ji-Feng Zhang.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Key R&D Program of China under Grant No. 2018YFA0703800, and the National Science Foundation of China under Grant No. T2293770.

This paper was recommended for publication by Editor HE Wei.

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Fu, S., Chen, L. & Zhang, JF. Stability in Inverse Problem of Determining Two Parameters for the Moore-Gibson-Thompson Equation with Memory Terms. J Syst Sci Complex 37, 2368–2389 (2024). https://doi.org/10.1007/s11424-024-3565-6

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  • DOI: https://doi.org/10.1007/s11424-024-3565-6

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