Kinetic Semidiscretization of Scalar Conservation Laws and Convergence by Using Averaging Lemmas∗
نویسنده
چکیده
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.
منابع مشابه
Averaging Lemmas and Dispersion Estimates for kinetic equations
Averaging lemmas consist in a regularizing effect on the average of the solution to a linear kinetic equation. Some of the main results are reviewed and their proofs presented in as self contained a way as possible. The use of kinetic formulations for the well posedness of scalar conservation laws is eventually explained as an example of application.
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