no. 5
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 5, pp. 1205-1223
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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 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.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/58
Classification : 35L65
Keywords: Nonlocal conservation laws, nonlocal flux, balance laws, singular limits, approximation of local conservation laws, entropy solution 
@article{AIHPC_2023__40_5_1205_0,
     author = {Coclite, Giuseppe Maria and Coron, Jean-Michel and De Nitti, Nicola and Keimer, Alexander and Pflug, Lukas},
     title = {A general result on the approximation of local conservation laws by nonlocal conservation laws: {The} singular limit problem for exponential kernels},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1205--1223},
     year = {2023},
     volume = {40},
     number = {5},
     doi = {10.4171/aihpc/58},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpc/58/}
}
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Coclite, Giuseppe Maria; Coron, Jean-Michel; De Nitti, Nicola; Keimer, Alexander; Pflug, Lukas. A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 5, pp. 1205-1223. doi: 10.4171/aihpc/58

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