existence and uniqueness of the solution of the coupled conduction-radiation energy transfer on diffuse-gray surfaces

This article gives very significant and up-to-date analytical results on the conductive-radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis of this work deals also with the question of existence and uniqueness of weak solution for this problem. The existence of weak solution will be proved by showing that our problem is pseudomonotone and coercive. The uniqueness of the solution will be proved using an idea from the analysis of nonlinear heat conduction.