Local Lipschitz Stability for Inverse Robin Problems in Some Elliptic and Parabolic Systems

TL;DR

This paper establishes local Lipschitz stability results for inverse Robin problems in elliptic and parabolic systems, providing a unified approach and extending previous results to parabolic cases.

Contribution

The paper introduces a new unified method for proving local Lipschitz stability in inverse Robin problems, generalizing previous elliptic results to parabolic systems.

Findings

Established local Lipschitz stability for elliptic inverse Robin problems.

Extended stability results to parabolic inverse Robin problems.

Reformulated existing arguments to unify the stability analysis.

Abstract

In this work, we shall study the nonlinear inverse problems of recovering the Robin coefficients in elliptic and parabolic systems of second order, and establish their local Lipschitz stabilities. Some local Lipschitz stability was derived for an elliptic inverse Robin problem. We shall first restructure the arguments in \cite{chou04} for the local Lipschitz stability so that the stability follows from three basic conditions for the elliptic inverse Robin problem. The new arguments are then generalized to help establish a novel local Lipschitz stability for parabolic inverse Robin problems.