' 2D-Local Existence and Uniqueness of a Transient State of a Coupled Radiative-Conductive Heat Transfer Problem

Mohamed Ghattassi (1) , Jean Rodolphe Roche (2) , Didier Schmitt (2) , Mohamed Boutayeb (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 EDP - Equations aux dérivées partielles

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.

Mots clés: Banach fixed point Theorem; Semi-transparent medium; Local existence-uniqueness; Nonlinear radiative-conductive heat transfer system

Domaines: Analyse numérique [math.NA]

Mohamed Ghattassi, Jean Rodolphe Roche, Didier Schmitt, Mohamed Boutayeb. ' 2D-Local Existence and Uniqueness of a Transient State of a Coupled Radiative-Conductive Heat Transfer Problem. 2016. ⟨hal-01272997v1⟩