Hydrodynamic limit for the Ginzburg–Landau ∇ϕ interface model with a conservation law and Dirichlet boundary conditions

Takao Nishikawa

Stochastic Processes and their Applications, 2017, vol. 127, issue 1, 228-272

Abstract: Hydrodynamic limit for the Ginzburg–Landau ∇ϕ interface model with a conservation law was established in Nishikawa (2002) under periodic boundary conditions. This paper studies the same problem on a bounded domain imposing the Dirichlet boundary condition. A nonlinear partial differential equation of fourth order satisfying the boundary conditions is derived as the macroscopic equation. Its solution converges to the Wulff shape derived by Deuschel et al. (2000) as the time t→∞.

Keywords: Ginzburg–Landau model; Effective interfaces; Massless fields (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spa.2016.06.007

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