KINETIC SEMIDISCRETIZATION OF SCALAR CONSERVATION LAWS AND CONVERGENCE BY USING AVERAGING LEMMAS

We consider a time discrete kinetic scheme (known as “transport collapse method”) for the inviscid Burgers equation ∂tu+ ∂x u 2 = 0. We prove the convergence of the scheme by using averaging lemmas without bounded variation estimate. Then, the extension of this result to the kinetic model of Brenier and Corrias is discussed.