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Hydrodynamic limit for ∇φ interface model on a wall
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  • Published: June 2003

Hydrodynamic limit for ∇φ interface model on a wall

  • Tadahisa Funaki1 

Probability Theory and Related Fields volume 126, pages 155–183 (2003)Cite this article

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Abstract.

 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.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914, Japan. e-mail: funaki@ms.u-tokyo.ac.jp, , , , , , JP

    Tadahisa Funaki

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  1. Tadahisa Funaki
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Additional information

Received: 10 January 2002 / Revised version: 18 August 2002 / Published online: 15 April 2003

Mathematics Subject Classification (2000): 60K35, 82C24, 35K55, 35K85

Key words or phrases: Hydrodynamic limit – Effective interfaces – Hard wall – Skorohod's stochastic differential equation – Evolutionary variational inequality

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Funaki, T. Hydrodynamic limit for ∇φ interface model on a wall. Probab. Theory Relat. Fields 126, 155–183 (2003). https://doi.org/10.1007/s00440-002-0238-y

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  • Issue Date: June 2003

  • DOI: https://doi.org/10.1007/s00440-002-0238-y

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Keywords

  • Differential Equation
  • Anisotropy
  • Partial Differential Equation
  • Variational Inequality
  • Periodic Boundary
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