The resonance behavior for the coupling of two Aw–Rascle traffic models
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Published:2020-02-07
Issue:1
Volume:2020
Page:
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ISSN:1687-1847
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Container-title:Advances in Difference Equations
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language:en
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Short-container-title:Adv Differ Equ
Author:
Hu Yanbo,Wang Guodong
Abstract
AbstractBy studying the Riemann problem for the Aw–Rascle traffic model with different pressure laws, which is the coupling of two one-dimensional hyperbolic systems, we investigate the resonance phenomena. The main difficulty arises from the possible resonance behavior which may result in multiple solutions. We discover a new and interesting phenomenon showing that there exist infinitely many solutions for some certain initial data, which is quite different compared to earlier studies for the isentropic model of a fluid flow in a nozzle with variable cross-section and the shallow water equations with discontinuous topography. In order to overcome this difficulty, we impose the so-called TV-condition to obtain the uniqueness of solution to the Riemann problem.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference39 articles.
1. Ambroso, A., Chalons, C., Coquel, F., Godlewski, E., Galié, T.: Interface model coupling via prescribed local flux balance. ESAIM: Math. Model. Numer. Anal. 48, 895–918 (2014) 2. Ambroso, A., Chalons, C., Coquel, F., Godlewski, E., Lagoutière, F., Raviart, P.A., Seguin, N.: A relaxation method for the coupling of systems of conservation laws. In: Hyperbolic Problem: Theory, Numerics, Applications, pp. 947–954. Springer, Berlin (2008) 3. Ambroso, A., Chalons, C., Coquel, F., Godlewski, E., Lagoutière, F., Raviart, P.A., Seguin, N.: Relaxation methods and coupling procedure. Int. J. Numer. Methods Fluids 56, 1123–1129 (2008) 4. Ambroso, A., Chalons, C., Coquel, F., Godlewski, E., Lagoutière, F., Raviart, P.A., Seguin, N.: Coupling of general Lagrangian systems. Math. Comput. 77, 909–941 (2008) 5. Andreianov, B., Karlsen, K.H., Risebro, H.N.: A theory of $L^{1}$-dissipative solvers for scalar conservation laws with discontinuous flux. Arch. Ration. Mech. Anal. 201, 27–86 (2011)
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