About Nucleation and Growth

  • A. Visintin
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)


Macroscopic and Mesoscopic Free Energies. Let us consider a substance capable of attaining two phases (solid and liquid, say), which occupies a bounded region Ω, ∈ R 3. Let us assume that the relative temperature is a prescribed function θ ∈ L∞(Ω), and set


Curvature Flow Prescribe Function Solid Ball Kinetic Undercooling Implicit Time Discretization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Almgren, F., Taylor, J.E., Wang, L. (1993) Curvature-driven flows: a variational approach. S.I.A.M. J. Control and Optimization 31 387–437MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Almgren, F., Wang, L. Mathematical existence of crystal growth with Gibbs-Thomson curvature effects. Journal of Geometric Analysis (to appear)Google Scholar
  3. 3.
    Buttazzo, G., Visintin, A. (eds.) (1994) Motion by Mean Curvature and Related Topics. De Gruyter, Berlin.zbMATHGoogle Scholar
  4. 4.
    Damlamian, A., Spruck, J., Visintin, A. (eds.) (1995) Curvature Flow and Related Problems. Gakkōtosho Scientific, Tokyo.Google Scholar
  5. 5.
    Luckhaus, S., Sturzenhecker, T. (1995) Implicit time discretization for the mean curvature flow equation. Calc. Var., 3 pp. 253–271MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Soner, M. (1995) Convergence of the phase-field equation to the Mullins-Sekerka problem with kinetic undercooling. Arch. Rational Mech. Anal., 131 pp. 139–197MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Visintin, (1998) A. Nucleation and mean curvature flow. Communications in P.D.E.s, 23, pp. 17–35MathSciNetzbMATHGoogle Scholar
  8. 8.
    Visintin, A., Stefan problem with nucleation and mean curvature flow, (in preparation)Google Scholar
  9. 9.
    Visintin, A., (1996) Models of Phase Transitions. Birkhäuser, Boston.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • A. Visintin
    • 1
  1. 1.Dipartimento di MatematicaPovo di TrentoItaly

Personalised recommendations