Abstract.
Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model was established in [6] under periodic boundary conditions. This paper studies the same problem on a bounded domain imposing Dirichlet boundary conditions. A nonlinear partial differential equation of second order with boundary conditions is derived as a macroscopic equation. The main tools are H − 1-method used in [6] and the higher integrability of gradients in [2].
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The author was supported by DFG project De 663/2-2 and 2/3 from April, 2001 to March, 2002, and by JSPS reserch fellowship for young scientists from April, 2002.
Mathematics Subject Classification (2000): 60K35, 82C24, 35K55
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Nishikawa, T. Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model with boundary conditions. Probab. Theory Relat. Fields 127, 205–227 (2003). https://doi.org/10.1007/s00440-003-0283-1
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DOI: https://doi.org/10.1007/s00440-003-0283-1
Key words or phrases:
- Hydrodynamic Limit
- Boundary Condition
- Ginzburg-Landau Model
- Effective Interfaces
- Massless Fields