Abstract

In this paper, we obtain BV estimates and L1 stability of solutions to a radiating gas model with nonlinear radiative inhomogeneity by using Lax-Friedrichs' scheme when a modified C-F-L (Courant-Friedrichs-Levy) condition is satisfied. Our result is a natural extension to that of the radiating gas model with linear radiative inhomogeneity so that it provides an understanding on the balance between nonlinear convection and nonlinear radiative inhomogeneity. The method for case of linear radiative inhomogeneity to obtain the key estimate on uniform bound does not work for the case of nonlinear radiative inhomogeneity. The difficulty is overcome by employing a simple but effective monotonic technic.

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