On an inverse boundary value problem for a nonlinear elastic wave equation

Gunther Uhlmann; Jian Zhai

doi:10.1016/j.matpur.2021.07.005

On an inverse boundary value problem for a nonlinear elastic wave equation

Gunther Uhlmann^*, Jian Zhai

^*Corresponding author for this work

HKUST Jockey Club Institute for Advanced Study

Research output: Contribution to journal › Journal Article › peer-review

34 Citations (Scopus)

Abstract

We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [1]. We show that all the parameters appearing in the equation can be uniquely determined from boundary measurements under certain geometric assumptions. The proof is based on second order linearization and Gaussian beams.

Original language	English
Pages (from-to)	114-136
Number of pages	23
Journal	Journal des Mathematiques Pures et Appliquees
Volume	153
DOIs	https://doi.org/10.1016/j.matpur.2021.07.005
Publication status	Published - Sept 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Masson SAS

Keywords

Elastic waves
Gaussian beams
Inverse boundary value problem
Nonlinear wave equation

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10.1016/j.matpur.2021.07.005

Cite this

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title = "On an inverse boundary value problem for a nonlinear elastic wave equation",

abstract = "We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [1]. We show that all the parameters appearing in the equation can be uniquely determined from boundary measurements under certain geometric assumptions. The proof is based on second order linearization and Gaussian beams.",

keywords = "Elastic waves, Gaussian beams, Inverse boundary value problem, Nonlinear wave equation",

author = "Gunther Uhlmann and Jian Zhai",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Masson SAS",

year = "2021",

month = sep,

doi = "10.1016/j.matpur.2021.07.005",

language = "English",

volume = "153",

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journal = "Journal des Mathematiques Pures et Appliquees",

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TY - JOUR

T1 - On an inverse boundary value problem for a nonlinear elastic wave equation

AU - Uhlmann, Gunther

AU - Zhai, Jian

PY - 2021/9

Y1 - 2021/9

N2 - We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [1]. We show that all the parameters appearing in the equation can be uniquely determined from boundary measurements under certain geometric assumptions. The proof is based on second order linearization and Gaussian beams.

AB - We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [1]. We show that all the parameters appearing in the equation can be uniquely determined from boundary measurements under certain geometric assumptions. The proof is based on second order linearization and Gaussian beams.

KW - Elastic waves

KW - Gaussian beams

KW - Inverse boundary value problem

KW - Nonlinear wave equation

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000685606000003

UR - https://openalex.org/W3183561620

UR - https://www.scopus.com/pages/publications/85111483478

U2 - 10.1016/j.matpur.2021.07.005

DO - 10.1016/j.matpur.2021.07.005

M3 - Journal Article

SN - 0021-7824

VL - 153

SP - 114

EP - 136

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

On an inverse boundary value problem for a nonlinear elastic wave equation

Abstract

Bibliographical note

Keywords

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