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

Coclite GM, Coron JM, De Nitti N, Keimer A, Pflug L (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Annales de l'Institut Henri Poincaré - Analyse Non Linéaire Elsevier Masson / Institute Henri Poincaré

Book Volume: 40

Pages Range: 1205-1223

Journal Issue: 5

DOI: 10.4171/AIHPC/58

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.L1loc/ 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.

Authors with CRIS profile

Nicola De Nitti Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Lukas Pflug Sonderforschungsbereich 814/3 Additive Fertigung

Involved external institutions

Politecnico di Bari IT Italy (IT) University of California, Berkeley US United States (USA) (US) Laboratoire Jacques-Louis Lions FR France (FR)

How to cite

APA:

Coclite, G.M., Coron, J.M., De Nitti, N., Keimer, A., & Pflug, L. (2023). A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 40(5), 1205-1223. https://dx.doi.org/10.4171/AIHPC/58

MLA:

Coclite, Giuseppe Maria, et al. "A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 40.5 (2023): 1205-1223.

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