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 ); BV (R)), which allows for discontinuities in the kernel.
On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels / Coclite, Giuseppe Maria; De Nitti, Nicola; Keimer, Alexander; Pflug, Lukas. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 73:6(2022), pp. 241-250. [10.1007/s00033-022-01766-0]
On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels
Coclite, Giuseppe Maria;
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 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 ); BV (R)), which allows for discontinuities in the kernel.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
