On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels

In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution γ ∗ q , we weaken the standard assumption on the kernel γ ∈ L ∞ ( ( 0 , T ) ; W 1 , ∞ ( R ) ) to the substantially...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2022-12, Vol.73 (6), Article 241
Main Authors: Coclite, Giuseppe Maria, De Nitti, Nicola, Keimer, Alexander, Pflug, Lukas
Format: Article
Language:English
Subjects:
Conservation laws
Engineering
Kernels
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Uniqueness
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Summary:In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution γ ∗ q , we weaken the standard assumption on the kernel γ ∈ L ∞ ( ( 0 , T ) ; W 1 , ∞ ( R ) ) to the substantially more general condition γ ∈ L ∞ ( ( 0 , T ) ; B V ( R ) ) , which allows for discontinuities in the kernel.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-022-01766-0