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arXiv · 2112.08847

Nonlinear semigroups for nonlocal conservation laws

Mihály Kovács·Mihály A. Vághy
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Abstract

We 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 Kru\v{z}kov-type nonlocal entropy inequality. Similarly to the local case, we demonstrate an efficient way of proving various desirable qualitative properties of the unique solution.

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Mihály Kovács, Mihály A. Vághy. 2021-12-16. Nonlinear semigroups for nonlocal conservation laws. https://arxiv.org/abs/2112.08847

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