Communications in Mathematical Physics

, Volume 118, Issue 1, pp 31-59

First online:

Nonlinear diffusion limit for a system with nearest neighbor interactions

  • M. Z. GuoAffiliated withDepartment of Mathematics, Beijing University
  • , G. C. PapanicolaouAffiliated withCourant Institute, New York University
  • , S. R. S. VaradhanAffiliated withCourant Institute, New York University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.