Convexification for the Viscocity Solution for a Coefficient Inverse Problem for the Radiative Transfer Equation
Numerical Analysis
2023-03-17 v2 Numerical Analysis
Abstract
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary value problem for the resulting system of two coupled partial differential equations. A Lipschitz stability estimate is proved for this boundary value problem using a Carleman estimate for the Laplace operator. Next, the global convergence analysis is provided via that Carleman estimate. Results of numerical experiments demonstrate a high computational efficiency of this approach.
Cite
@article{arxiv.2302.12474,
title = {Convexification for the Viscocity Solution for a Coefficient Inverse Problem for the Radiative Transfer Equation},
author = {Michael V. Klibanov and Jingzhi Li and Zhipeng Yang},
journal= {arXiv preprint arXiv:2302.12474},
year = {2023}
}