Nonlinear diffusion limit for a system with nearest neighbor interactions. II. (English) Zbl 0793.60105

Varadhan, S. R. S.

Elworthy, K. D. (ed.) et al., Asymptotic problems in probability theory: stochastic models and diffusions on fractals. Proceedings of the 26th Taniguchi international symposium, Sanda and Kyoto, Japan, August 31 - September 5, 1990. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 283, 75-128 (1993).

This paper is a continuation to the previous one with M. Z. Guo and G. C. Papanicolaou [Commun. Math. Phys. 118, No. 1, 31-59 (1988; Zbl 0652.60107)]. In the development of the study on the hydrodynamic limits, the previous paper has played a critical role, in which the entropy method was introduced. In the present paper, the constant diffusion coefficient is extended to the uniform elliptic one. Certainly, such an extension contains some difficulties.
For the entire collection see [Zbl 0780.00028].

Reviewer: Chen Mu-fa (Beijing)

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60J60	Diffusion processes

Keywords:

entropy estimates; local Gibbs states; interacting diffusions; weak solution of a nonlinear diffusion equation; hydrodynamic limits

Citations:

Zbl 0652.60107