The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • textscS. Allen and textscJ. Cahn. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. phActa Metall. 27, no. 6, (1979), 1085--1095.
  • Albeverio, S.; Röckner, M. Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms. Probab. Theory Related Fields 89 (1991), no. 3, 347--386. MR1113223
  • Barret, Florent; Bovier, Anton; Méléard, Sylvie. Uniform estimates for metastable transition times in a coupled bistable system. Electron. J. Probab. 15 (2010), no. 12, 323--345. MR2609590
  • textscH. Bahouri, textscJ. Chemin, and textscR. Danchin. phFourier analysis and nonlinear partial differential equations, vol. 343 of phGrundlehren der mathematischen Wissenschaften Series. Springer Verlag, 2010.
  • Cerrai, Sandra; Freidlin, Mark. Approximation of quasi-potentials and exit problems for multidimensional RDE's with noise. Trans. Amer. Math. Soc. 363 (2011), no. 7, 3853--3892. MR2775830
  • Da Prato, Giuseppe; Debussche, Arnaud. Strong solutions to the stochastic quantization equations. Ann. Probab. 31 (2003), no. 4, 1900--1916. MR2016604
  • textscG. Da~Prato and textscL. Tubaro. Wick powers in stochastic PDEs: an introduction. phTechnical Report UTM 711, University of Trento (2007).
  • Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136
  • Evans, L. C.; Soner, H. M.; Souganidis, P. E. Phase transitions and generalized motion by mean curvature. Comm. Pure Appl. Math. 45 (1992), no. 9, 1097--1123. MR1177477
  • Glimm, James; Jaffe, Arthur. Quantum physics. A functional integral point of view. Second edition. Springer-Verlag, New York, 1987. xxii+535 pp. ISBN: 0-387-96476-2 MR0887102
  • textscM. Hairer. An introduction to stochastic PDEs. rlhttp://www. hairer. org/Teaching. html, 2009. Unpublished lecture notes.
  • Ilmanen, Tom. Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature. J. Differential Geom. 38 (1993), no. 2, 417--461. MR1237490
  • Kohn, Robert; Otto, Felix; Reznikoff, Maria G.; Vanden-Eijnden, Eric. Action minimization and sharp-interface limits for the stochastic Allen-Cahn equation. Comm. Pure Appl. Math. 60 (2007), no. 3, 393--438. MR2284215
  • textscL. Landau, and textscL. Ginzburg. On the theory of superconductivity. phJ. Expt. Theor. Phys. 20, (1950), 1064--1082.
  • Parisi, G.; Wu, Yong Shi. Perturbation theory without gauge fixing. Sci. Sinica 24 (1981), no. 4, 483--496. MR0626795
  • textscM.D. Ryser, textscN. Nigam, and textscP.F. Tupper. On the well-posedness of the stochastic Allen-Cahn equation in two dimensions. phJ. Comp. Phys. 231, no. 6, (2012), 2537--2550.
  • Walsh, John B. An introduction to stochastic partial differential equations. École d'été de probabilités de Saint-Flour, XIV—1984, 265--439, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876085
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.