# Existence and Uniqueness of a Transient State for the Coupled Radiative-Conductive Heat Transfer Problem

## TL;DR

This paper establishes the existence and uniqueness of solutions for a complex three-dimensional transient radiative-conductive heat transfer system, using fixed-point theory to handle the nonlinear coupled equations.

## Contribution

It provides the first rigorous proof of existence and uniqueness for this class of nonlinear radiative-conductive heat transfer problems in three dimensions.

## Key findings

- Existence of solutions proved using Banach fixed point theorem.
- Uniqueness of solutions established under certain conditions.
- The reformulation as a fixed-point problem facilitates analysis.

## Abstract

This paper deals with existence and uniqueness results for a transient nonlinear radiative-conductive system in three-dimensional case. This system describes the heat transfer for a grey, semi-transparent and non-scattering medium with general boundary conditions. We reformulate the full transient state system as a fixed-point problem. The existence and uniqueness proof is based on Banach fixed point theorem.