Hydrodynamic limit for ∇φ interface model on a wall |
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Authors: | Tadahisa Funaki |
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Institution: | (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 |
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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.
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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