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Recovery of Coefficients in Semilinear Transport Equations

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Abstract

We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a stable way, from the boundary measurements, by applying a linearization scheme and Carleman estimates for the linear transport equations. We establish results in both Euclidean and general geometry settings.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Ru-Yu Lai

  2. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Gunther Uhlmann

  3. HKUST Jockey Club Institute for Advanced Study, HKUST, Clear Water Bay, Kowloon, Hong Kong

    Gunther Uhlmann

  4. Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA

    Hanming Zhou

Authors
  1. Ru-Yu Lai
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  2. Gunther Uhlmann
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  3. Hanming Zhou
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Corresponding author

Correspondence to Hanming Zhou.

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Conflict of interest

Ru-Yu Lai is partially supported by the National Science Foundation through grant DMS-2006731 and DMS-2306221. Gunther Uhlmann is partly supported by NSF, a Simons Fellowship, a Walker Family Professorship at UW, and a Si Yuan Professorship at IAS, HKUST. Hanming Zhou is partly supported by the NSF grant DMS-2109116.

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Communicated by T.-P. Liu.

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Lai, RY., Uhlmann, G. & Zhou, H. Recovery of Coefficients in Semilinear Transport Equations. Arch Rational Mech Anal 248, 62 (2024). https://doi.org/10.1007/s00205-024-02007-6

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  • DOI: https://doi.org/10.1007/s00205-024-02007-6

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