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Bibliographic Details
Main Author: Johansson, David
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2412.14817
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author Johansson, David
author_facet Johansson, David
contents We study an inverse boundary value problem in corrosion detection. The model is based on a conductivity equation with nonlinear Robin boundary condition. We prove that the nonlinear Robin term can be identified locally from Cauchy data measurements on a subset of the boundary. A possible strategy for turning a local identification result into a global one is suggested, and a partial result is proved in this direction. The inversion method is an adaptation to this nonlinear Robin problem of a method originally developed for semilinear elliptic equations. The strategy is based on linearization and relies on parametrizing solutions of the nonlinear equation on solutions of the linearized equation.
format Preprint
id arxiv_https___arxiv_org_abs_2412_14817
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Corrosion detection by identification of a nonlinear Robin boundary condition
Johansson, David
Analysis of PDEs
We study an inverse boundary value problem in corrosion detection. The model is based on a conductivity equation with nonlinear Robin boundary condition. We prove that the nonlinear Robin term can be identified locally from Cauchy data measurements on a subset of the boundary. A possible strategy for turning a local identification result into a global one is suggested, and a partial result is proved in this direction. The inversion method is an adaptation to this nonlinear Robin problem of a method originally developed for semilinear elliptic equations. The strategy is based on linearization and relies on parametrizing solutions of the nonlinear equation on solutions of the linearized equation.
title Corrosion detection by identification of a nonlinear Robin boundary condition
topic Analysis of PDEs
url https://arxiv.org/abs/2412.14817