Nonlocal scalar conservation laws with discontinuous flux-Reference-Cited by-同舟云学术

Nonlocal scalar conservation laws with discontinuous flux

Published:2022 Issue:1 Volume:18 Page:380-398
ISSN:1556-1801
Container-title:Networks and Heterogeneous Media
language:
Short-container-title:NHM

Author:

Chiarello Felisia Angela¹,Coclite Giuseppe Maria²

Affiliation:

1. Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica (DISIM), University of L'Aquila, Via Vetoio, 67100 L'Aquila, Italy

2. Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Via E. Orabona 4, 70125 Bari, Italy

Abstract

<abstract><p>We prove the well-posedness of entropy weak solutions for a class of space-discontinuous scalar conservation laws with nonlocal flux. We approximate the problem adding a viscosity term and we provide $ {{\bf{L}}^\infty} $ and BV estimates for the approximate solutions. We use the doubling of variable technique to prove the stability with respect to the initial data from the entropy condition.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability

Reference28 articles.

1. J. Aleksić, D. Mitrović, Strong traces for averaged solutions of heterogeneous ultra-parabolic transport equations, J. Hyperbolic Differ. Equ., 10 (2013), 659–676. https://doi.org/10.1142/S0219891613500239

2. S. W. Amadori Debora, An integro-differential conservation law arising in a model of granular flow, J. Hyperbolic Differ. Equ., 9 (2012), 105–131.

3. B. Andreianov, K. H. Karlsen, N. H. Risebro, On vanishing viscosity approximation of conservation laws with discontinuous flux, Netw. Heterog. Media, 5 (2010), 617–633. https://doi.org/10.3934/nhm.2010.5.617

4. B. Andreianov, D. Mitrović, Entropy conditions for scalar conservation laws with discontinuous flux revisited, Ann. Inst. H. Poincaré Anal. Non Linéaire, 32 (2015), 1307–1335. https://doi.org/10.1016/j.anihpc.2014.08.002

5. C. Bardos, A. Y. le Roux, J. C. Nédélec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, 4 (1979), 1017–1034. https://doi.org/10.1080/03605307908820117

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

1. Convergence of the numerical approximations and well-posedness: Nonlocal conservation laws with rough flux;Mathematics of Computation;2024-05-13

2. A non-local traffic flow model for 1-to-1 junctions with buffer;Networks and Heterogeneous Media;2024

3. Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity;Comptes Rendus. Mathématique;2023-12-21

4. Convergence of a second-order scheme for non-local conservation laws;ESAIM: Mathematical Modelling and Numerical Analysis;2023-11

5. Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux;Journal of Engineering Mathematics;2023-07-28