Hölder stability in determining the potential and the damping coefficient in a wave equation

Abstract

We improve the preceding results obtained by Ammari and Choulli (J Differ Equ 259(7):3344–3365, 2015). They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an initial-to-boundary operator. We partially modify the arguments in Ammari and Choulli  (2015) to show that actually we have a local Hölder stability instead of logarithmic stability.

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Acknowledgements

We would like to thank the referee for his valuable comments which enabled us to improve substantially the paper.

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Correspondence to Kaïs Ammari.

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FT is partially supported by LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01).

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Ammari, K., Choulli, M. & Triki, F. Hölder stability in determining the potential and the damping coefficient in a wave equation. J. Evol. Equ. 19, 305–319 (2019). https://doi.org/10.1007/s00028-018-0476-9

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Mathematics Subject Classification

  • 35R30

Keywords

  • Inverse problem
  • Hölder stability
  • Wave equation
  • Damping coefficient
  • Potential