BV Estimates on Lax–Friedrichs' Scheme or a Model of Radiating Gas

In this article, we give a uniform BV estimates and L 1-stability of solutions to the Lax–Friedrichs' scheme for a model of radiating gas when the strict C–F–L (Courant–Friedrichs–Levy) condition is satisfied. This result implies that the approximate solutions generated by the Lax–Friedrichs' scheme converge to the solution given by the method of vanishing viscosity [C. Lattanzio and P. Marcati (2003 Lattanzio, C and Marcati, P. 2003. Global well-posedness and relaxation limits of a model for radiating gas. Journal of Differential Equations, 190: 439–465. [Crossref], [Web of Science ®] , [Google Scholar]). Global well-posedness and relaxation limits of a model for radiating gas. Journal of Differential Equations, 190, 439–465].