Abstract
AbstractWe investigate a class of nonlocal conservation laws in several space dimensions, where the continuum average of weighted nonlocal interactions are considered over a finite horizon. We establish well-posedness for a broad class of flux functions and initial data via semigroup theory in Banach spaces and, in particular, via the celebrated Crandall–Liggett Theorem. We also show that the unique mild solution satisfies a Kružkov-type nonlocal entropy inequality. Similarly to the local case, we demonstrate an efficient way of proving various desirable qualitative properties of the unique solution.
Funder
Marsden Fund
Vetenskapsrådet
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
Nemzeti Kutatási, Fejlesztési és Innovaciós Alap
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis,Analysis
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