Corrosion detection by identification of a nonlinear Robin boundary condition

2024/12/19 by David Johansson, Johansson, David · 1 citation
Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Non-Destructive Testing Techniques #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.2412.14817

openalex publication_date 2024/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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