We consider the identification of a nonlinear corrosion profile from single voltage boundary data and show injectivity of the parameter-to-output map. We demonstrate that Tikhonov regularization can be applied in order to solve the inverse problem in a stable manner despite the presence of noisy data. In combination with a logarithmic stability estimate for the underlying Cauchy problem, rates for the convergence of the regularized solutions are proven using a source condition that does not involve the Fréchet derivative of the parameter-to-output map. We present sufficient conditions for the existence of a source function and illustrate our approach by means of numerical examples

Logarithmic convergence rates for the identification of a nonlinear Robin coefficient

SINCICH, EVA
2009-01-01

Abstract

We consider the identification of a nonlinear corrosion profile from single voltage boundary data and show injectivity of the parameter-to-output map. We demonstrate that Tikhonov regularization can be applied in order to solve the inverse problem in a stable manner despite the presence of noisy data. In combination with a logarithmic stability estimate for the underlying Cauchy problem, rates for the convergence of the regularized solutions are proven using a source condition that does not involve the Fréchet derivative of the parameter-to-output map. We present sufficient conditions for the existence of a source function and illustrate our approach by means of numerical examples
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2540353
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