Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model with boundary conditions
Download PDF
Download PDF
  • Published: 04 July 2003

Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model with boundary conditions

  • Takao Nishikawa1 

Probability Theory and Related Fields volume 127, pages 205–227 (2003)Cite this article

  • 109 Accesses

  • 4 Citations

  • Metrics details

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].

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Chang, C.C., Yau, H.-T.: Fluctuations of one dimensional Ginzburg-Landau models in nonequilibrium. Commun. Math. Phys. 145, 209–239 (1992)

    MathSciNet  MATH  Google Scholar 

  2. Deuschel, J.-D., Giacomin, G., Ioffe, D.: Large deviations and concentration properties for ∇ϕ interface models. Probab. Theory Relat. Fields 117, 49–111 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dobrushin, R.L., Kotecký, S.B., Shlosman, S.: Wulff construction: a global shape from local interaction. AMS translation series 104, 115–137 (1992)

    Google Scholar 

  4. Eyink, G., Lebowitz, J.L., Spohn, H.: Lattice gas models in contact with stochastic reservoirs: local equilibrium and relaxation to the steady states. Commun. Math. Phys. 140, 119–131 (1991)

    MathSciNet  MATH  Google Scholar 

  5. Funaki, T., Sakagawa, H.: Large deviations for ∇ϕ interface model and derivation of free boundary problems, preprint, 2002

  6. Funaki, T., Spohn, H.: Motion by mean curvature from the Ginzburg-Landau ∇φ interface model. Commun. Math. Phys. 185, 1–36 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton~University~Press, 1981

  8. Guo, M.Z., Papanicolaou, G.C., Varadhan, S.R.S.: Nonlinear diffusion limit for a system with nearest neighbor interactions. Commun. Math. Phys. 118, 31–59 (1988)

    MathSciNet  MATH  Google Scholar 

  9. Spohn, H.: Interface motion in models with stochastic dynamics. J. Stat. Phys. 71, 1081–1132 (1993)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Takao Nishikawa

Authors
  1. Takao Nishikawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takao Nishikawa.

Additional information

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

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received: 31 August 2002

  • Revised: 25 April 2003

  • Published: 04 July 2003

  • Issue Date: October 2003

  • DOI: https://doi.org/10.1007/s00440-003-0283-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Key words or phrases:

  • Hydrodynamic Limit
  • Boundary Condition
  • Ginzburg-Landau Model
  • Effective Interfaces
  • Massless Fields
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature