Reconstruction of the emission coefficient in the nonlinear radiative transfer equation

TL;DR

This paper addresses an inverse problem for a coupled radiative transfer and heat equation system, demonstrating unique reconstruction of the emission coefficient from surface measurements using a single experiment setup.

Contribution

It introduces a novel method to uniquely recover the nonlinear emission coefficient in a coupled radiative transfer and heat system with minimal experimental data.

Findings

Unique reconstruction of the emission coefficient from surface measurements.

Reconstruction requires only one experiment setup.

The method applies to nonscattering media in multiple dimensions.

Abstract

In this paper, we investigate an inverse problem for the radiative transfer equation that is coupled with a heat equation in a nonscattering medium in $\mathbb{R}^n$, $n\geq 2$. The two equations are coupled through a nonlinear blackbody emission term that is proportional to the fourth power of the temperature. By measuring the radiation intensity on the surface of the blackbody, we prove that the emission property of the system can be uniquely reconstructed. In particular, we design a reconstruction procedure that uses merely one set of experiment setup to fully recover the emission parameter.