Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity

Keimer A, Pflug L (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Comptes Rendus Mathematique Elsevier Masson

Book Volume: 361

Pages Range: 1723-1760

Journal Issue: G11

DOI: 10.5802/crmath.490

Abstract

We study nonlocal conservation laws with a discontinuous flux function of regularity L^∞(R) in the spatial variable and show existence and uniqueness of weak solutions in C¡[0,T];L¹loc^¢, as well as related maximum principles. We achieve this well-posedness by a proper reformulation in terms of a fixed-point problem. This fixed-point problem itself necessitates the study of existence, uniqueness and stability of a class of discontinuous ordinary differential equations. On the ODE level, we compare the solution type defined here with the well-known Carathéodory and Filippov solutions.

Authors with CRIS profile

Lukas Pflug Lehrstuhl für Angewandte Mathematik (Kontinuierliche Optimierung)

Additional Organisation(s)

FAU Competence Center Scientific Computing (FAU CSC)

Involved external institutions

University of California, Berkeley

United States (USA) (US)

How to cite

APA:

Keimer, A., & Pflug, L. (2023). Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity. Comptes Rendus Mathematique, 361(G11), 1723-1760. https://doi.org/10.5802/crmath.490

MLA:

Keimer, Alexander, and Lukas Pflug. "Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity." Comptes Rendus Mathematique 361.G11 (2023): 1723-1760.

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