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

Abstract

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). Global well-posedness and relaxation limits of a model for radiating gas. Journal of Differential Equations, 190, 439–465].

Keywords:

• Lax–Friedrichs' scheme
• BV solution
• L1-stability
• Radiating gas
• AMS Subject Classifications: 35L60
• 35L65
• 65N12

Acknowledgments

The research of the first author was supported by the Strategic Research Grant of City University of Hong Kong, #7001330. The research of the second author was supported by a grant from the National Natural Science Foundation of China (The Youth Foundation).

Notes

^†E-mail: [email protected]

Additional information

Notes on contributors

Huijiang Zhao †

†E-mail: [email protected]