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

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arxiv 2311.14528 v1 pith:6GLATDXR submitted 2023-11-24 math.AP

Maria Colombo , Gianluca Crippa , Elio Marconi , Laura V. Spinolo This is my paper · ORCID
classification math.AP
keywords conservationlimitlocalnon-localcompactnessconvolutionestimateoverview
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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.

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  1. Nonlocal-to-local limit for linear transport equations with measure initial data

    math.AP 2026-07 conditional novelty 6.0 of 10

    Solutions of the nonlocal linear transport equation ∂_t u^ε + B·∇(η_ε*u^ε)=0 converge to the local transport equation ∂_t u + B·∇u=0 as ε→0 for measure initial data and in arbitrary dimension.

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