Abstract
AbstractIn 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 $$\gamma *q$$
γ
∗
q
, we weaken the standard assumption on the kernel $$\gamma \in L^\infty \big ((0,T); W^{1,\infty }({\mathbb {R}})\big )$$
γ
∈
L
∞
(
(
0
,
T
)
;
W
1
,
∞
(
R
)
)
to the substantially more general condition $$\gamma \in L^\infty ((0,T); BV({\mathbb {R}}))$$
γ
∈
L
∞
(
(
0
,
T
)
;
B
V
(
R
)
)
, which allows for discontinuities in the kernel.
Funder
Friedrich-Alexander-Universität Erlangen-Nürnberg
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Physics and Astronomy,General Mathematics
Reference44 articles.
1. Aletti, G., Naldi, G., Toscani, G.: First-order continuous models of opinion formation. SIAM J. Appl. Math. 67(3), 837–853 (2007)
2. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000)
3. Bayen, A., Coron, J.-M., De Nitti, N., Keimer, A., Pflug, L.: Boundary controllability and asymptotic stabilization of a nonlocal traffic flow model. Vietnam J. Math. 49(3), 957–985 (2021)
4. Bayen, A., Friedrich, J., Keimer, A., Pflug, L., Veeravalli, T.: Modeling multi-lane traffic with moving obstacles by nonlocal balance laws. SIAM J. Appl. Dyna. Syst 21(2) (2022)
5. Betancourt, F., Bürger, R., Karlsen, K.H., Tory, E.M.: On nonlocal conservation laws modelling sedimentation. Nonlinearity 24(3), 855–885 (2011)
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献