Stationary thermography can be used for investigating the functional form of a nonlinear cooling lawthat describes heat exchanges through an inaccessible part of the boundary of a conductor. In this paper, we obtain a logarithmic stability estimate for the associated nonlinear inverse problem. This stability estimate is obtained from the convergence and sensitivity analysis of a finite difference method for the numerical solution of the Cauchy problem for Laplace's equation, based on the Störmer-Verlet scheme.
Recovering nonlinear terms in an inverse boundary value problem for Laplace's equation: A stability estimate
Inglese G
2007
Abstract
Stationary thermography can be used for investigating the functional form of a nonlinear cooling lawthat describes heat exchanges through an inaccessible part of the boundary of a conductor. In this paper, we obtain a logarithmic stability estimate for the associated nonlinear inverse problem. This stability estimate is obtained from the convergence and sensitivity analysis of a finite difference method for the numerical solution of the Cauchy problem for Laplace's equation, based on the Störmer-Verlet scheme.File in questo prodotto:
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