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Recovery of Nonlinear Terms for Reaction Diffusion Equations from Boundary Measurements

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Abstract

In the present article we study the inverse problem of determining a general semilinear term for a class of nonlinear parabolic equations. We derive a new criterion for the unique and stable recovery of general semilinear terms for these type of equations from the knowledge of the parabolic Dirichlet-to-Neumann map associated with solutions of the equation having zero initial data.

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Acknowledgements

The work of Y.K is partially supported by the French National Research Agency ANR (project MultiOnde) grant ANR-17-CE40-0029. The research of G.U. is partially supported by NSF, a Walker Professorship at UW and a Si-Yuan Professorship at IAS, HKUST. Part of the work was supported by the NSF grant DMS-1440140 while G.U. were in residence at MSRI in Berkeley, California, during Fall 2019 semester.

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Authors and Affiliations

  1. Aix Marseille Univ, CNRS, CPT Université de Toulon, Marseille, France

    Yavar Kian

  2. Department of Mathematics University of Washington, Seattle, WA, 98195-4350, USA

    Gunther Uhlmann

  3. Institute for Advanced Study of the Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

    Gunther Uhlmann

Authors
  1. Yavar Kian
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  2. Gunther Uhlmann
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Correspondence to Gunther Uhlmann.

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Communicated by D. Kinderlehrer.

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Kian, Y., Uhlmann, G. Recovery of Nonlinear Terms for Reaction Diffusion Equations from Boundary Measurements. Arch Rational Mech Anal 247, 6 (2023). https://doi.org/10.1007/s00205-022-01831-y

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