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

摘要

Stationary thermography can be used for investigating the functional form of a nonlinear cooling law that 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.