BV-estimates of Lax-Friedrichs scheme for hyperbolic conservation laws with relaxation

In this paper, we will give BV-estimates of Lax-Friedrichsʹ scheme for a simple hyperbolic system of conservation laws with relaxation and get the global existence and uniqueness of BV-solution by the BV-estimates above. Furthermore, our results show that the solution converge towards the solution of an equilibrium model as the relaxation time (epsilon)>0 tends to zero provided sub-characteristic condition holds.