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

Coclite GM, De Nitti N, Keimer A, Pflug L (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Zeitschrift für Angewandte Mathematik und Physik Springer Verlag (Germany)

Book Volume: 73

Article Number: 241

Journal Issue: 6

DOI: 10.1007/s00033-022-01766-0

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) ; W¹^,^∞(R)) to the substantially more general condition γ∈ L^∞((0 , T) ; BV(R)) , which allows for discontinuities in the kernel.

Authors with CRIS profile

Nicola De Nitti Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Lukas Pflug FAU Competence Center Scientific Computing (FAU CSC)

Involved external institutions

Politecnico di Bari

Italy (IT) University of California, Berkeley

United States (USA) (US)

How to cite

APA:

Coclite, G.M., De Nitti, N., Keimer, A., & Pflug, L. (2022). On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels. Zeitschrift für Angewandte Mathematik und Physik, 73(6). https://dx.doi.org/10.1007/s00033-022-01766-0

MLA:

Coclite, Giuseppe Maria, et al. "On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels." Zeitschrift für Angewandte Mathematik und Physik 73.6 (2022).

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