Free Access
Issue
ESAIM: M2AN
Volume 37, Number 1, January/February 2003
Page(s) 117 - 132
DOI https://doi.org/10.1051/m2an:2003017
Published online 15 March 2003
  1. S. Allen and J. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979) 1084-1095. [Google Scholar]
  2. H. Brezis, Analyse fonctionnelle. Masson, Paris (1983). Théorie et applications [Theory and applications]. [Google Scholar]
  3. Xinfu Chen, Generationand propagation of interfaces for reaction-diffusion equations. J. Differential Equations 96 (1992) 116-141. [Google Scholar]
  4. E.A. Coddington and N. Levinson, Theory of ordinary differential equations. McGraw-Hill Book Company, Inc., New York, Toronto, London (1955). [Google Scholar]
  5. Ha Dang, P.C. Fife and L.A. Peletier, Saddle solutions of the bistable diffusion equation. Z. Angew. Math. Phys. 43 (1992) 984-998. [CrossRef] [MathSciNet] [Google Scholar]
  6. F.R. de Hoog and R. Weiss, An approximation theory for boundary value problems on infinite intervals. Computing 24 (1980) 227-239. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. de Mottoni and M. Schatzman, Development of interfaces in Formula . Proc. Roy. Soc. Edinburgh Sect. A 116 (1990) 207-220. [MathSciNet] [Google Scholar]
  8. P. de Mottoni and M. Schatzman, Geometrical evolution of developed interfaces. Trans. Amer. Math. Soc. 347 (1995) 1533-1589. [CrossRef] [MathSciNet] [Google Scholar]
  9. B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves. Math. Comp. 31 (1977) 629-651. [CrossRef] [MathSciNet] [Google Scholar]
  10. L.C. Evans, H.M. Soner and P.E. Souganidis, Phase transitions and generalized motion by mean curvature. Comm. Pure Appl. Math. 45 (1992) 1097-1123. [Google Scholar]
  11. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition. [Google Scholar]
  12. T.M. Hagstrom and H.B. Keller, Asymptotic boundary conditions and numerical methods for nonlinear elliptic problems on unbounded domains. Math. Comp. 48 (1987) 449-470. [CrossRef] [MathSciNet] [Google Scholar]
  13. T. Hagstrom and H.B. Keller, Exact boundary conditions at an artificial boundary for partial differential equations in cylinders. SIAM J. Math. Anal. 17 (1986) 322-341. [CrossRef] [MathSciNet] [Google Scholar]
  14. T. Ilmanen, Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature. J. Differential Geom. 38 (1993) 417-461. [MathSciNet] [Google Scholar]
  15. A.D. Jepson and H.B. Keller, Steady state and periodic solution paths: their bifurcations and computations, in Numerical methods for bifurcation problems, Dortmund (1983). Birkhäuser, Basel (1984) 219-246. [Google Scholar]
  16. A. Jepson, Asymptotic boundary conditions for ordinary differential equations. Ph.D. thesis, California Institute of Technology (1980). [Google Scholar]
  17. P.A. Markowich, A theory for the approximation of solutions of boundary value problems on infinite intervals. SIAM J. Math. Anal. 13 (1982) 484-513. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Schatzman, On the stability of the saddle solution of Allen-Cahn's equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 1241-1275. [MathSciNet] [Google Scholar]

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