4.5 Article

THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE NON-ISENTROPIC IMPROVED AW-RASCLE-ZHANG MODEL

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

On the stability of the improved Aw-Rascle-Zhang model with Chaplygin pressure

Tingting Chen et al.

Summary: This paper investigates the stability of the Riemann problem for the improved Aw-Rascle-Zhang model, which describes the formation and dynamics of traffic jams. By constructing classical Riemann solutions and analyzing wave interactions, the existence and uniqueness of delta-shock wave in this model are proven, leading to stability analysis of the Riemann problem.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2021)

Article Mathematics

Existence and Uniqueness of the Global L1 Solution of the Euler Equations for Chaplygin Gas

Tingting Chen et al.

Summary: This paper establishes the global existence and uniqueness of the solution of the Cauchy problem of a one-dimensional compressible isentropic Euler system for a Chaplygin gas with large initial data. The method used is Lagrangian representation with characteristic analysis, and the assumptions on the initial data are believed to be necessary for ruling out the formation of Dirac singularity of density. The ideas and techniques developed here may be useful for other nonlinear problems involving similar difficulties.

ACTA MATHEMATICA SCIENTIA (2021)

Article Mathematics, Applied

Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas

Aifang Qu et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2020)

Article Physics, Mathematical

General limiting behavior of Riemann solutions to the non-isentropic Euler equations for modified Chaplygin gas

Yating Song et al.

JOURNAL OF MATHEMATICAL PHYSICS (2020)

Article Mathematics, Applied

The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations with a source term

Lihui Guo et al.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2018)

Article Mechanics

The non-self-similar Riemann solutions to a compressible fluid described by the generalized Chaplygin gas

Yicheng Pang et al.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS (2018)

Article Mathematics, Applied

Delta shock wave in the compressible Euler equations for a Chaplygin gas

Yicheng Pang

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2017)

Article Engineering, Multidisciplinary

Developing an Aw-Rascle model of traffic flow

Wei-Feng Jiang et al.

JOURNAL OF ENGINEERING MATHEMATICS (2016)

Article Engineering, Multidisciplinary

Fuzzy Prediction for Traffic Flow Based on Delta Test

Yang Wang et al.

MATHEMATICAL PROBLEMS IN ENGINEERING (2016)

Article Mathematics, Applied

The comparison of the Riemann solutions in gas dynamics

Wei-Feng Jiang et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2015)

Article Mathematics, Applied

Stability of the Riemann solutions for a Chaplygin gas

Qu Aifang et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2014)

Article Mathematics, Applied

The Aw-Rascle traffic model with Chaplygin pressure

Lijun Pan et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2013)

Article Mathematics, Applied

Multidimensional Shock Interaction for a Chaplygin Gas

Denis Serre

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2009)

Article Mathematics, Applied

INTERACTIONS OF ELEMENTARY WAVES FOR THE AW-RASCLE MODEL

Meina Sun

SIAM JOURNAL ON APPLIED MATHEMATICS (2009)

Article Mathematics, Applied

A model for the formation and evolution of traffic jams

F. Berthelin et al.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2008)

Article Mathematics, Applied

The Riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws

Hanchun Yang et al.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2007)

Article Economics

The Aw-Rascle and Zhang's model: Vacuum problems, existence and regularity of the solutions of the Riemann problem

Jean-Patrick Lebacque et al.

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL (2007)

Article Mathematics, Applied

A hybrid lagrangian model based on the aw-rascle traffic flow model

S. Moutari et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2007)

Article Mathematics, Applied

Traffic flow on a road network using the aw-rascle model

M Garavello et al.

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2006)

Article Mathematics, Applied

Coupling conditions for a class of second-order models for traffic flow

M. Herty et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2006)

Article Mathematics, Applied

Nonlinear dynamics of traffic jams

T Li

PHYSICA D-NONLINEAR PHENOMENA (2005)

Article Mathematics, Applied

Solutions with concentration to the Riemann problem for the one-dimensional chaplygin gas equations

Y Brenier

JOURNAL OF MATHEMATICAL FLUID MECHANICS (2005)

Article Mathematics, Applied

Congestion on multilane highways

JM Greenberg et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2003)

Article Mathematics, Applied

Extensions and amplifications of a traffic model of Aw and Rascle

JM Greenberg

SIAM JOURNAL ON APPLIED MATHEMATICS (2002)

Article Economics

A non-equilibrium traffic model devoid of gas-like behavior

HM Zhang

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL (2002)

Article Mathematics, Applied

Resurrection of second order models of traffic flow

A Aw et al.

SIAM JOURNAL ON APPLIED MATHEMATICS (2000)