# Convexification for the Viscocity Solution for a Coefficient Inverse Problem for the Radiative Transfer Equation

## TL;DR

This paper introduces a convexification method for a coefficient inverse problem in radiative transfer, incorporating viscosity solutions and proving stability and convergence, with numerical results showing high efficiency.

## Contribution

It is the first to consider viscosity solutions for the boundary value problem in this context and provides stability and convergence analysis using Carleman estimates.

## Key findings

- Proved Lipschitz stability for the boundary value problem.
- Established global convergence of the numerical method.
- Numerical experiments demonstrate high computational efficiency.

## 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.