Hydrodynamic limit for ∇φ interface model on a wall

Tadahisa Funaki*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We consider random evolution of an interface on a hard wall under periodic boundary conditions. The dynamics are governed by a system of stochastic differential equations of Skorohod type, which is Langevin equation associated with massless Hamiltonian added a strong repelling force for the interface to stay over the wall. We study its macroscopic behavior under a suitable large scale space-time limit and derive a nonlinear partial differential equation, which describes the mean curvature motion except for some anisotropy effects, with reflection at the wall. Such equation is characterized by an evolutionary variational inequality.

Original languageEnglish
Pages (from-to)155-183
Number of pages29
JournalProbability Theory and Related Fields
Issue number2
Publication statusPublished - 2003 Jun
Externally publishedYes


  • Effective interfaces
  • Evolutionary variational inequality
  • Hard wall
  • Hydrodynamic limit
  • Skorohod's stochastic differential equation

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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