The zero relaxation limit for the hydrodynamic Whitham traffic flow model

Journal of Differential Equations

Volumn 141, Issue 1, 1997, Pages 150-178

  Lattanzio, Corrado ^a   Marcati, Pierangelo ^a  

^a UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031581268     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3311     Document Type: Article

References (16)

1. 1. G.-Q. Chen, C. D. Levermore, and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994), 787-830.
2. 2. G.-Q. Chen and Y. Lu, The study on application way of the compensated compactness theory, Chin. Sci. Bull. 34 (1989), 15-19.
3. 3. G. Q. Chen, X. Ding, and P. Luo, Convergence of the Law-Friedrichs scheme for isentropic gas dynamics I-II, Acta Math. Sci. 5 (1985), 415-472.
4. 4. K. N. Chueh, C. C. Conley, and J. A. Smoller, Positively invariant regions for systems of non-linear diffusion equations, Indiana Univ. Math. J. 26 (1977), 372-411.
5. 5. R. J. DiPerna, Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91 (1983), 1-30.
6. 6. R. J. DiPerna, Measure-valued solutions to conservation laws, Arch. Rational Mech. Anal. 88 (1985), 223-270.
7. 7. S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995), 235-276.
8. 8. S. Kružkov, First order quasi-linear equations with several space variables, Mat. Sb. 123 (1970), 228-255.
9. 9. P. L. Lions, B. Perthame, and P. E. Souganidis, Existence and stability of entropy solutions for the hyperbolic systems or isentropic gas dynamics in Eulerian and Lagrangian coordinates, Comm. Pure Appl. Math. 49 (1996), 599.
10. 10. T.-P. Liu, Hyperbolic conservation laws with relaxation, Comm. Math. Phys. 108 (1987), 153-175.
11. 11. P. Marcati, Relaxation and singular convergence for quasilinear hyperbolic systems, in "First Italian-Spain Meeting on Nonlinear Analisis" (L. Boccardo, M. A. Herrero, and A. Tesei, Eds.), pp. 140-148, Quaderno IAC-CNR, Rome, 1989.
12. -1,q est compacte pour tout q < 2, Math. Pure Appl. 60 (1981), 309-322.
13. 13. R. Natalini, Convergence to equilibrium for the relaxation approximation of conservation laws, Comm. Pure Appl. Math. 49 (1996), 795-823.
14. 14. S. Schochet, The instant-response limit in Whitham's nonlinear traffic-flow model: Uniform well-posedness and global existence, Asymptotic Anal. 1 (1988), 263-282.
15. 15. A. Szepessy, An existence result for scalar conservation laws using measure valued solutions, Comm. Partial Differential Equations 14 (1989), 1329-1350.
16. 16. G. B. Whitham, "Linear and Nonlinear Waves," Wiley, New York, 1974.