A bounded variation estimate for the force scheme applied to strictly hyperbolic systems of conservation laws in the temple class

摘要

Bressan and Jenssen established a uniform bounded variation (BV) estimate for the Godunov scheme for Temple-type strictly hyperbolic systems of conservation laws and gave a proof based on the probability theory of random walks. In this paper, we provide a different proof which is simpler and does not use any probability theory. Applying our theory, we establish a uniform BV estimate for the Force scheme for the same class of hyperbolic systems, under the assumption of small total variation of initial data.