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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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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DOI: https://doi.org/10.1007/s00440-002-0238-y
Keywords
- Differential Equation
- Anisotropy
- Partial Differential Equation
- Variational Inequality
- Periodic Boundary