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

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

1 IECL - Institut Élie Cartan de Lorraine
2 CRAN - Centre de Recherche en Automatique de Nancy

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; Local existence-uniqueness; Semi-transparent medium; 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-01272997v2⟩