The zero relaxation limit for the hydrodynamic Whitham traffic flow model

DOI10.1006/jdeq.1997.3311zbMath0907.35132OpenAlexW2085168250WikidataQ58619791 ScholiaQ58619791MaRDI QIDQ1377546

Pierangelo Marcati, Corrado Lattanzia

Publication date: 26 January 1998

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1997.3311

zbMATH Keywords

entropy solutions\(L^\infty\) estimatesrelaxation phenomenaexistence of weak entropy solutionsKružkov-type entropy conditionsrate of convergence toward the equilibrium

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

Traffic Flow on a Road Network Using the Aw–Rascle Model, Generalized Riemann problems and exact solutions for \(p\)-systems with relaxation, A relaxation scheme for conservation laws with a discontinuous coefficient, Nonstrictly hyperbolic systems with stiff relaxation terms, Global existence of classical solutions for the gas flows near vacuum through ducts expanding with space and time, On the role of source terms in continuum traffic flow models, Global well-posedness and asymptotic behavior of \(BV\) solutions to a system of balance laws arising in traffic flow, Uniform boundedness in weak solutions to a specific dissipative system, Existence and non-existence of global smooth solutions for \(p\)-system with relaxation, Global BV solutions to a \(p\)-system with relaxation, The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model, Analysis of non-isentropic compressible Euler equations with relaxation, Initial boundary value problem for compressible Euler equations with relaxation, Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data, Conservation laws for $2 \times 2 $ hyperbolic systems, Nonlinear dynamics of traffic jams, Singular limits of stiff relaxation and dominant diffusion for nonlinear systems, An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model

Cites Work

• Convergence of the viscosity method for isentropic gas dynamics
• Hyperbolic conservation laws with relaxation
• The embedding of the positive cone of $H^{-1}$ in $W^{-1,\,q}$ is compact for all $q<2$ (with a remark of Haim Brezis)
• Measure-valued solutions to conservation laws
• The study on application way of the compensated compactness theory
• An existence result for scalar conservation laws using measure valued solutions.
• Hyperbolic conservation laws with stiff relaxation terms and entropy
• The relaxation schemes for systems of conservation laws in arbitrary space dimensions
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