Singular limits with vanishing viscosity for nonlocal conservation laws

Coclite GM, De Nitti N, Keimer A, Pflug L (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Nonlinear Analysis - Theory Methods & Applications Elsevier

Book Volume: 211

Article Number: 112370

DOI: 10.1016/j.na.2021.112370

Abstract

We consider a class of nonlocal conservation laws with a second-order viscous regularization term which finds an application in modelling macroscopic traffic flow. The velocity function depends on a weighted average of the density ahead, where the averaging kernel is of exponential type. We show that, as the nonlocal impact and the viscosity parameter simultaneously tend to zero (under a suitable balance condition), the solution of the nonlocal problem converges to the entropy solution of the corresponding local conservation law. The key ideas of our proof are to observe that the nonlocal term satisfies a third-order equation with diffusive and dispersive effects and to deduce a suitable energy estimate on the nonlocal term. The convergence result is then based on the compensated compactness theory.

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

University of California, Berkeley

United States (USA) (US) Politecnico di Bari

Italy (IT)

How to cite

APA:

Coclite, G.M., De Nitti, N., Keimer, A., & Pflug, L. (2021). Singular limits with vanishing viscosity for nonlocal conservation laws. Nonlinear Analysis - Theory Methods & Applications, 211. https://dx.doi.org/10.1016/j.na.2021.112370

MLA:

Coclite, Giuseppe Maria, et al. "Singular limits with vanishing viscosity for nonlocal conservation laws." Nonlinear Analysis - Theory Methods & Applications 211 (2021).

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