Existence results for a nonlinear coupled radiative–conductive heat transfer system

Abstract

In this paper, we present existence results for a one-dimensional coupled system of nonlinear integro-differential equations on Lp-spaces with 1≤p<∞. This system describes the steady-state combined radiative–conductive heat transfer. We reformulate the full coupled system as a fixed point problem. This formulation is applied to prove existence results for the radiation intensity and the temperature fields. We treat separately the cases p=1 and p>1. The analysis for p>1 uses the Krasnosel’skii fixed point theorem, while the existence results in the case p=1 are obtained via a new variant of that theorem for the weak topology established in Latrach et al. (2006).