Recovering nonlinear terms in an inverse boundary value problem for Laplace's equation: a stability estimate

DOI10.1016/j.cam.2005.07.026zbMath1145.65091OpenAlexW2056140772MaRDI QIDQ2508953

Dario Fasino, Gabriele Inglese

Publication date: 20 October 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.07.026

zbMATH Keywords

nonlinear boundary conditionsCauchy problem for Laplace equationcorrosion detectionlogarithmic stability estimatesStörmer-Verlet scheme

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items (1)

Corrosion detection in a 2D domain with a polygonal boundary

Cites Work

• STABILITY OF THE SOLUTIONS OF AN INVERSE PROBLEM FOR LAPLACE'S EQUATION IN A THIN STRIP
• A survey of computational efforts in the field of corrosion engineering
• Logarithmic Convexity for Discrete Harmonic Functions and the Approximation of the Cauchy Problem for Poisson's Equation
• Nonlinear elliptic boundary-value problems in unbounded domains
• Discrete methods in the study of an inverse problem for Laplace's equation
• Stability and Regularization of a Discrete Approximation to the Cauchy Problem for Laplace's Equation
• An inverse problem in corrosion detection
• Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling
• Stable determination of corrosion by a single electrostatic boundary measurement
• Logarithmic stability estimates for a Robin coefficient in two-dimensional Laplace inverse problems
• A nonlinear elliptic boundary value problem related to corrosion modeling
• On the existence and ‘blow-up’ of solutions to a two-dimensional nonlinear boundary-value problem arising in corrosion modelling
• Identification of Robin coefficients by the means of boundary measurements
• Detecting nonlinear corrosion by electrostatic measurements
• Recovering unknown terms in a nonlinear boundary condition for Laplace's equation
• On a Priori Bounds in the Cauchy Problem for Elliptic Equations
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