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Nonlinear diffusion limit for a system with nearest neighbor interactions

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Abstract

We consider a system of interacting diffusions. The variables are to be thought of as charges at sites indexed by a periodic one-dimensional lattice. The diffusion preserves the total charge and the interaction is of nearest neighbor type. With the appropriate scaling of lattice spacing and time, a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density.

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Authors and Affiliations

  1. Department of Mathematics, Beijing University, Beijing, People's Republic of China

    M. Z. Guo

  2. Courant Institute, New York University, 251 Mercer Street, 10012, New York, NY, USA

    G. C. Papanicolaou & S. R. S. Varadhan

Authors
  1. M. Z. Guo
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  2. G. C. Papanicolaou
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  3. S. R. S. Varadhan
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Additional information

Communicated by J. L. Lebowitz

Work supported by the National Science Foundation under grants no. DMS 8600233 and DMS 8701895

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Guo, M.Z., Papanicolaou, G.C. & Varadhan, S.R.S. Nonlinear diffusion limit for a system with nearest neighbor interactions. Commun.Math. Phys. 118, 31–59 (1988). https://doi.org/10.1007/BF01218476

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  • DOI: https://doi.org/10.1007/BF01218476

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