Cakoni, F. and Kress, R. (2007) Integral Equations for Inverse Problems in Corrosion Detection from Partial Cauchy Data. Inverse Problems and Imaging, 1, 229-245.
https://doi.org/10.3934/ipi.2007.1.229

has been cited by the following article:

• TITLE: Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints

  AUTHORS: Weifu Fang, Fu-Rong Lin

  KEYWORDS: Robin Inverse Problem, Ill-Posed Problem, Laplace Equation, Boundary Inte-gral Equation, Nonnegativity Constraint, Penalty Method

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.6, June 30, 2022

  ABSTRACT: We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.