Nonlinear diffusion limit for a system with nearest neighbor interactions

M. Z. Guo; G. C. Papanicolaou; S. R.S. Varadhan

doi:10.1007/BF01218476

Nonlinear diffusion limit for a system with nearest neighbor interactions

M. Z. Guo, G. C. Papanicolaou, S. R.S. Varadhan

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	31-59
Number of pages	29
Journal	Communications In Mathematical Physics
Volume	118
Issue number	1
DOIs	https://doi.org/10.1007/BF01218476
State	Published - Mar 1988

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01218476

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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.",

author = "Guo, {M. Z.} and Papanicolaou, {G. C.} and Varadhan, {S. R.S.}",

year = "1988",

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AB - 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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Nonlinear diffusion limit for a system with nearest neighbor interactions

Abstract

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