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Hydrodynamic limit for particle systems with nonconstant speed parameter

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Abstract

We establish the hydrodynamic limit for a class of particle systems on ℤd with nonconstant speed parameter, assuming that the speed parameter is continuously differentiable in the spatial variable. If the particle system is on the one-dimensional latticeℤ and totally asymmetric, we derive the hydrodynamic equation for continuous speed parameters. We obtain nontrivial upper and lower bounds when either the speed parameter is discontinuous or there is a blockage at a fixed site.

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References

  • [A] E. D. Andjel, Invariant measures for the zero range process,Ann. Prob. 10:525–547 (1982).

    MATH  MathSciNet  Google Scholar 

  • [C] C. T. Cocozza, Processus des misanthropes,Z. Wahrs. Verw. Gebiete 70:509–523 (1985).

    Article  Google Scholar 

  • [D] R. J. DiPerna, Measure-valued solutions to conservation laws,Arch. Rational Mech. Anal. 88:223–270 (1985).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • [DZ] A. Dembo and O. Zeitouni,Large Deviations and Applications (Boston, London, Jones and Bartlett, 1993).

    Google Scholar 

  • [ES] L. C. Evans and P. E. Souganidis, Differential Games and Representation Formulas for Solution of Hamilton-Jacobi-Isaacs Equations,Indiana Univ. Math. J. 33:773–797 (1984).

    Article  MathSciNet  Google Scholar 

  • [JL1] S. Janowsky and J. Lebowitz, Finite size effects and shock fluctuations in the asymmetric simple exclusion process,Phys. Rev. A 45:618–625 (1992).

    Article  ADS  Google Scholar 

  • [JL2] S. Janowsky and J. Lebowitz, Exact results for the asymmetric simple exclusion process with a blockage,J. Stat. Phys. 77:35–51 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  • [K] S. N. Kružkov, First order quaslinear equations is several independent variables,Math. USSR-Sb. 10:217–243 (1970).

    Article  Google Scholar 

  • [La] C. Landim, Hydrodynamical limit for space inhomogeneous one dimensional totally asymmetric zero range processes, to appear in Annals of Probability.

  • [Li] T. M. Liggett,Interacting Particle Systems (Berlin, Heidelberg, New York, Springer, 1985).

    MATH  Google Scholar 

  • [OVY] S. Olla, S. R. S. Varadhan, and H. T. Yau, Hydrodynamical limit for a Hamiltanian system with weak noise,Commun. Math. Phys. 155:523–560 (1993).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • [R] F. Rezakhanlou, Hydrodynamic limit for interacting particle systems on Zd,Commun. Math. Phys. 140:417–448 (1991).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • [Y] H. T. Yau, Relative entropy and hydrodynamics of Ginsburg-Landau models,Letters Math. Phys. 22:63–80 (1991).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720-3840, Berkeley, California

    Paul Covert & Fraydoun Rezakhanlou

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  1. Paul Covert
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  2. Fraydoun Rezakhanlou
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Covert, P., Rezakhanlou, F. Hydrodynamic limit for particle systems with nonconstant speed parameter. J Stat Phys 88, 383–426 (1997). https://doi.org/10.1007/BF02508477

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  • DOI: https://doi.org/10.1007/BF02508477

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