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An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate

Colombo, Maria and Crippa, Gianluca and Marconi, Elio and Spinolo, Laura V.. (2024) An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate. Preprints Fachbereich Mathematik, 2024 (04).

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Abstract

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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Crippa, Gianluca
Item Type:Preprint
Publisher:Universität Basel
Language:English
edoc DOI:
Last Modified:19 Jun 2024 06:21
Deposited On:19 Jun 2024 06:21

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