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@article{faucris.314060134,
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.L^{1}loc/ 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.},
author = {Coclite, Giuseppe Maria and Coron, Jean Michel and De Nitti, Nicola and Keimer, Alexander and Pflug, Lukas},
doi = {10.4171/AIHPC/58},
faupublication = {yes},
journal = {Annales de l'Institut Henri PoincarĂ© - Analyse Non LinĂ©aire},
keywords = {approximation of local conservation laws; balance laws; entropy solution; Nonlocal conservation laws; nonlocal flux; singular limits},
note = {CRIS-Team Scopus Importer:2023-11-17},
pages = {1205-1223},
peerreviewed = {Yes},
title = {{A} general result on the approximation of local conservation laws by nonlocal conservation laws: {The} singular limit problem for exponential kernels},
volume = {40},
year = {2023}
}