Existence and uniqueness of solutions of nonlinear systems of conductive-radiative heat transfer equations

Abstract

We prove an existence and uniqueness results for a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. Our approach uses two different formulations of the system as a compact fixed-point problem. One formulation, which has been used in numerical work, is used for uniqueness and a new one is used for the existence proof.

Key Words:

• radiative-conductive heat transfer
• compact fixed point problems
• existence-uniqueness

AMS subject classifications:

• 45G10
• 45K05
• 82A70