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An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate (2311.14528v1)
Published 24 Nov 2023 in math.AP
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.