An Inverse Source Problem Related to Acoustic Nonlinearity Parameter Imaging

Masahiro Yamamoto () and Barbara Kaltenbacher ()
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Masahiro Yamamoto: The University of Tokyo, Komaba, Graduate School of Mathematical Sciences
Barbara Kaltenbacher: Alpen-Adria-Universität Klagenfurt, Department of Mathematics

A chapter in Time-dependent Problems in Imaging and Parameter Identification, 2021, pp 413-456 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-57784-1_14

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DOI: 10.1007/978-3-030-57784-1_14

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