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.
@incollection{JEDP_2023____A10_0, author = {Maria Colombo and Gianluca Crippa and Elio Marconi and Laura V. Spinolo}, title = {An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, note = {talk:10}, pages = {1--14}, publisher = {R\'eseau th\'ematique AEDP du CNRS}, year = {2023}, doi = {10.5802/jedp.681}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.681/} }
TY - JOUR AU - Maria Colombo AU - Gianluca Crippa AU - Elio Marconi AU - Laura V. Spinolo TI - An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate JO - Journées équations aux dérivées partielles N1 - talk:10 PY - 2023 SP - 1 EP - 14 PB - Réseau thématique AEDP du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.681/ DO - 10.5802/jedp.681 LA - en ID - JEDP_2023____A10_0 ER -
%0 Journal Article %A Maria Colombo %A Gianluca Crippa %A Elio Marconi %A Laura V. Spinolo %T An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate %J Journées équations aux dérivées partielles %Z talk:10 %D 2023 %P 1-14 %I Réseau thématique AEDP du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.681/ %R 10.5802/jedp.681 %G en %F JEDP_2023____A10_0
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), Talk no. 10, 14 p. doi : 10.5802/jedp.681. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.681/
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