Existence theory for one-dimensional quasilinear coupled conductive–radiative flows

• We solve the conductive–radiative problem with a temperature dependent on the diffusion coefficient.
• We use techniques of monotonicity in order to yield the solution of the problem.
• We solve the problem with the Green Function Decomposition method.
• We make the existence theory for quasilinear conductive–radiative problem.

The paper deals with the coupled conductive–radiative problem with a diffusion coefficient depending on the temperature. The technique of upper and lower solutions is used to generate a solution for this nonlinear problem in the space of Hölder continuous function by Pao (1992,2007) [1,2] together with certain integral representations given in Azevedo et al. (2011) [3]. We also produce numerical results using GFDNGFDN method, the Green Function Decomposition of the order N  , coupled with the Crank–Nicolson method and the Newton–Raphson method. The GFDNGFDN methodology arises from the integral representation involved and does not involve any a priori discretization on the angular variable μμ.