An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate
Maria Colombo1 ; Gianluca Crippa2 ; Elio Marconi3 ; Laura V. Spinolo4
1 EPFL B, Station 8 CH-1015 Lausanne, Switzerland
2 Departement Mathematik und Informatik Universität Basel Spiegelgasse 1, CH-4051 Basel, Switzerland
3 Dipartimento di Matematica “Tullio Levi-Civita” Università degli Studi di Padova via Trieste 63, 35131 Padua, Italy
4 CNR-IMATI “E. Magenes” via Ferrata 5, I-27100 Pavia, Italy
Journées équations aux dérivées partielles (2023), Exposé no. 10, 14 p.

Consider a non-local (i.e., involving a convolution term) conservation law: when the convolution term converges to a Dirac delta, in the limit we formally recover a classical (or “local”) conservation law. In this note we overview recent progress on this so-called non-local to local limit and in particular we discuss the case of anistropic kernels, which is extremely relevant in view of applications to traffic models. We also provide a new proof of a related compactness estimate.

Publié le :
DOI : 10.5802/jedp.681
Classification : 35L65
Keywords: non-local to local limit, non-local conservation laws, singular local limit, traffic models.

Maria Colombo 1 ; Gianluca Crippa 2 ; Elio Marconi 3 ; Laura V. Spinolo 4

1 EPFL B, Station 8 CH-1015 Lausanne, Switzerland
2 Departement Mathematik und Informatik Universität Basel Spiegelgasse 1, CH-4051 Basel, Switzerland
3 Dipartimento di Matematica “Tullio Levi-Civita” Università degli Studi di Padova via Trieste 63, 35131 Padua, Italy
4 CNR-IMATI “E. Magenes” via Ferrata 5, I-27100 Pavia, Italy 
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Maria Colombo; Gianluca Crippa; Elio Marconi; Laura V. Spinolo. An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate. Journées équations aux dérivées partielles (2023), Exposé no. 10, 14 p. doi : 10.5802/jedp.681. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.681/

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