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 gamma * q, we weaken the standard assumption on the kernel gamma is an element of L-infinity((0, T); W-1,W-infinity(R)) to the substantially more general condition gamma is an element of L-infinity((0, T); BV (R)), which allows for discontinuities in the kernel.
On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels
De Nitti N
;
2022-01-01
Abstract
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 gamma * q, we weaken the standard assumption on the kernel gamma is an element of L-infinity((0, T); W-1,W-infinity(R)) to the substantially more general condition gamma is an element of L-infinity((0, T); BV (R)), which allows for discontinuities in the kernel.File in questo prodotto:
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