2D-local existence and uniqueness of a transient state of a coupled radiative-conductive heat transfer problem

This paper deals with local existence and uniqueness results for a transient two-dimensional combined nonlinear radiative-conductive system. This system describes the heat transfer for a grey, semi-transparent and non-scattering medium with homogeneous Dirichlet boundary conditions. We reformulate the full transient state system as a fixed-point problem. The existence and uniqueness proof rests upon the Banach fixed-point Theorem assuming the initial data T 0 is non-negative and sufficiently small.