A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels

  • Giuseppe Maria Coclite

    Politecnico di Bari, Italy
  • Jean-Michel Coron

    Université Pierre et Marie Curie, Paris, France
  • Nicola De Nitti

    Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
  • Alexander Keimer

    University of California, Berkeley, United States of America
  • Lukas Pflug

    Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels cover
Download PDF

A subscription is required to access this article.

Abstract

We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential-type approximation of the Dirac distribution. We then obtain a total variation bound on the nonlocal term and can prove that the (unique) weak solution of the nonlocal problem converges strongly in C(Lloc1)C({L_{loc}^{1}}) to the entropy solution of the local conservation law. We conclude with several numerical illustrations which underline the main results and, in particular, the difference between the solution and the nonlocal term.

Cite this article

Giuseppe Maria Coclite, Jean-Michel Coron, Nicola De Nitti, Alexander Keimer, Lukas Pflug, A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels. Ann. Inst. H. Poincaré Anal. Non Linéaire (2022),

DOI 10.4171/AIHPC/58