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

2023/11/24 by Colombo, Maria, Crippa, Gianluca, Marconi, Elio +1 · 4 citations
#35L65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.14528

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.

Cited by

• Optimal Control Problems with Nonlocal Conservation Laws: Existence of Optimizers and Singular Limits in Approximations of Local Conservation Laws
• Well-posedness of multidimensional nonlocal conservation laws with nonlinear mobility and bounded force
• Control of Conservation Laws in the Nonlocal-to-Local Limit
• Asymptotically compatible entropy-consistent discretization for a class of nonlocal conservation laws

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