On the Cahn-Hilliard equation
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Tài liệu tham khảo
R. A. Adams, Sobolev Spaces, Academic Press, New York (1975).
J. W. Cahn & J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958), 258–267.
J. Carr, M. E. Gurtin & M. Slemrod, Structural phase transitions on a finite interval, Arch. Rational Mech. Anal. 12 (1984), 317–351.
D. S. Cohen & J. D. Murray, A generalized diffusion model for growth and dispersal in a population, J. Math. Biology 12 (1981), 237–249.
J. Douglas, Jr., T. Dupont & L. Wahlbin, Optimal L ∞ error estimates for Galerkin approximations to solutions of two point boundary value problems, Math. Comp. 29 (1975), 475–483.
M. Hazewinkel, J. F. Kaashoek & B. Leynse, Pattern formation for a one dimensional evolution equation based on Thom's river basin model, Report # 8519/B, Econometric Institute, Erasmus University (1985).
S. Klainerman & G. Ponce, Global small amplitude solutions to nonlinear evolution equations, Comm. Pure. Appl. Math. 36 (1983), 133–141.
J. L. Lions & E. Magenes, Non-homogeneous boundary value problems and applications, Vol. II, Springer-Verlag (1972).
A. Novick-Cohen, Energy methods for the Cahn-Hilliard equation, IMA Preprint # 157, (1985).
A. Novick-Cohen & L. A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica 10 (D) (1984), 277–298.
G. I. Sivashinsky, On cellular instability in the solidification of a dilute binary alloy, Physica 8 (D) (1983), 243–248.
V. Thomée, Some convergence results for Galerkin methods for parabolic boundary value problems, in Mathematical Aspects of Finite Element Methods in Partial Differential Equations, ed. C. de Boor, Academic Press (1974), p. 55–84.
V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, L. N. M. # 1054, Springer-Verlag, Berlin (1984).
L. Wahlbin, On maximum norm error estimates for Galerkin approximations to one dimensional second order parabolic boundary value problems, SIAM J. Numer. Anal. 12 (1975), 177–187.