Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear semigroups for nonlocal conservation laws   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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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc