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An Inverse Source Problem Related to Acoustic Nonlinearity Parameter Imaging

In: Time-dependent Problems in Imaging and Parameter Identification

Author

Listed:
  • Masahiro Yamamoto

    (The University of Tokyo, Komaba, Graduate School of Mathematical Sciences
    Academy of Romanian Scientists
    Peoples’ Friendship University of Russia (RUDN University))

  • Barbara Kaltenbacher

    (Alpen-Adria-Universität Klagenfurt, Department of Mathematics)

Abstract

In this article, we discuss an inverse source problem of determining a spatially varying factor of a source term in a linearized higher order model of nonlinear acoustics, which is a partial differential equation of the third order in time and the fourth order in space. We establish two kinds of stability for the inverse source problems: (1) space-local stability of Hölder type and (2) space-global stability of Lipschitz type. Our key is two types of Carleman estimates with a regular and a singular weight functions.

Suggested Citation

  • Masahiro Yamamoto & Barbara Kaltenbacher, 2021. "An Inverse Source Problem Related to Acoustic Nonlinearity Parameter Imaging," Springer Books, in: Barbara Kaltenbacher & Thomas Schuster & Anne Wald (ed.), Time-dependent Problems in Imaging and Parameter Identification, pages 413-456, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-57784-1_14
    DOI: 10.1007/978-3-030-57784-1_14
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