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Volumn 67, Issue 11, 2007, Pages 3176-3193

Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy

Author keywords

Cahn Hilliard equation; Convergence to steady states; Logarithmic potential; Lojasiewicz Simon inequality; Monotone operators

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FREE ENERGY; MATHEMATICAL OPERATORS; PHASE EQUILIBRIA;

EID: 34547595689     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.10.002     Document Type: Article
Times cited : (155)

References (22)
  • 1
    • 1842592819 scopus 로고    scopus 로고
    • A fourth-order parabolic equation with a logarithmic nonlinearity
    • Bonfoh A. A fourth-order parabolic equation with a logarithmic nonlinearity. Bull. Austral. Math. Soc. 69 (2004) 35-48
    • (2004) Bull. Austral. Math. Soc. , vol.69 , pp. 35-48
    • Bonfoh, A.1
  • 2
    • 0003282411 scopus 로고
    • Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
    • North-Holland Publishing Co., Amsterdam Notas de Matemática (50)
    • Brézis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Mathematics Studies vol. 5 (1973), North-Holland Publishing Co., Amsterdam Notas de Matemática (50)
    • (1973) North-Holland Mathematics Studies , vol.5
    • Brézis, H.1
  • 3
    • 33746012315 scopus 로고    scopus 로고
    • Free energy of a nonuniform system. I. interfacial energy
    • Cahn J.W., and Hilliard J.E. Free energy of a nonuniform system. I. interfacial energy. J. Chem. Phys. 28 2 (2005) 258-267
    • (2005) J. Chem. Phys. , vol.28 , Issue.2 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 4
    • 0004011487 scopus 로고    scopus 로고
    • The Clarendon Press Oxford University Press, New York Translated from the 1990 French original by Yvan Martel and revised by the authors
    • Cazenave T., and Haraux A. An Introduction to Semilinear Evolution Equations. Oxford Lecture Series in Mathematics and its Applications vol. 13 (1998), The Clarendon Press Oxford University Press, New York Translated from the 1990 French original by Yvan Martel and revised by the authors
    • (1998) Oxford Lecture Series in Mathematics and its Applications , vol.13
    • Cazenave, T.1    Haraux, A.2
  • 5
    • 0038116267 scopus 로고    scopus 로고
    • On the Łojasiewicz-Simon gradient inequality
    • Chill R. On the Łojasiewicz-Simon gradient inequality. J. Funct. Anal. 201 2 (2003) 572-601
    • (2003) J. Funct. Anal. , vol.201 , Issue.2 , pp. 572-601
    • Chill, R.1
  • 6
    • 33749673101 scopus 로고    scopus 로고
    • Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions
    • Chill R., Fašangová E., and Prüss J. Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions. Math. Nachr. 279 13-14 (2006) 1448-1462
    • (2006) Math. Nachr. , vol.279 , Issue.13-14 , pp. 1448-1462
    • Chill, R.1    Fašangová, E.2    Prüss, J.3
  • 7
    • 0029307671 scopus 로고
    • On the Cahn-Hilliard equation with a logarithmic free energy
    • Debussche A., and Dettori L. On the Cahn-Hilliard equation with a logarithmic free energy. Nonlinear Anal. 24 10 (1995) 1491-1514
    • (1995) Nonlinear Anal. , vol.24 , Issue.10 , pp. 1491-1514
    • Debussche, A.1    Dettori, L.2
  • 8
    • 0034251772 scopus 로고    scopus 로고
    • A singularly perturbed phase field model with a logarithmic nonlinearity: Upper-semicontinuity of the attractor
    • (5-6, Ser. A: Theory Methods)
    • Dupaix C. A singularly perturbed phase field model with a logarithmic nonlinearity: Upper-semicontinuity of the attractor. Nonlinear Anal. 41 (2000) 725-744 (5-6, Ser. A: Theory Methods)
    • (2000) Nonlinear Anal. , vol.41 , pp. 725-744
    • Dupaix, C.1
  • 9
    • 34547612628 scopus 로고    scopus 로고
    • C.M. Elliot, S. Luckhaus, A generalized equation for phase separation of a multi-component mixture with interfacial free energy, 1991. preprint SFB 256 Bonn No. 195
  • 11
    • 0030526461 scopus 로고    scopus 로고
    • On the Cahn-Hilliard equation with degenerate mobility
    • Elliott C.M., and Garcke H. On the Cahn-Hilliard equation with degenerate mobility. SIAM J. Math. Anal. 27 2 (1996) 404-423
    • (1996) SIAM J. Math. Anal. , vol.27 , Issue.2 , pp. 404-423
    • Elliott, C.M.1    Garcke, H.2
  • 12
    • 13844316920 scopus 로고    scopus 로고
    • On a Cahn-Hilliard model for phase separation with elastic misfit
    • Garcke H. On a Cahn-Hilliard model for phase separation with elastic misfit. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005) 165-185
    • (2005) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.22 , pp. 165-185
    • Garcke, H.1
  • 13
    • 34250247917 scopus 로고
    • r spaces
    • r spaces. Math. Z. 178 (1981) 297-329
    • (1981) Math. Z. , vol.178 , pp. 297-329
    • Giga, Y.1
  • 14
    • 0041625080 scopus 로고    scopus 로고
    • Elliptic partial differential equations of second order
    • Springer-Verlag, Berlin Reprint of the 1998 edition
    • Gilbarg D., and Trudinger N.S. Elliptic partial differential equations of second order. Classics in Mathematics (2001), Springer-Verlag, Berlin Reprint of the 1998 edition
    • (2001) Classics in Mathematics
    • Gilbarg, D.1    Trudinger, N.S.2
  • 16
    • 0347556781 scopus 로고
    • Subdifferential operator approach to the Cahn-Hilliard equation with constraint
    • Kenmochi N., Niezgódka M., and Pawlow I. Subdifferential operator approach to the Cahn-Hilliard equation with constraint. J. Differential Equations 117 (1995) 320-354
    • (1995) J. Differential Equations , vol.117 , pp. 320-354
    • Kenmochi, N.1    Niezgódka, M.2    Pawlow, I.3
  • 17
    • 1642337137 scopus 로고    scopus 로고
    • Robust exponential attractors for Cahn-Hilliard type equations with singular potentials
    • Miranville A., and Zelik S. Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Math. Methods Appl. Sci. 27 5 (2004) 545-582
    • (2004) Math. Methods Appl. Sci. , vol.27 , Issue.5 , pp. 545-582
    • Miranville, A.1    Zelik, S.2
  • 18
    • 34250762267 scopus 로고    scopus 로고
    • Maximal regularity and asymptotic behaviour of solutions for the Cahn-Hilliard equation with dynamic boundary conditions
    • Prüss J., Racke R., and Zheng S. Maximal regularity and asymptotic behaviour of solutions for the Cahn-Hilliard equation with dynamic boundary conditions. Ann. Mat. Pura Appl. 185 4 (2006) 627-648
    • (2006) Ann. Mat. Pura Appl. , vol.185 , Issue.4 , pp. 627-648
    • Prüss, J.1    Racke, R.2    Zheng, S.3
  • 19
    • 34250750395 scopus 로고    scopus 로고
    • p-regularity and long-time behaviour of the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions
    • Partial Differential Equations and Functional Analysis, Birkhäuser, Basel
    • p-regularity and long-time behaviour of the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions. Partial Differential Equations and Functional Analysis. Operator Theory: Advances and Applications vol. 168 (2006), Birkhäuser, Basel 209-236
    • (2006) Operator Theory: Advances and Applications , vol.168 , pp. 209-236
    • Prüss, J.1    Wilke, M.2
  • 20
    • 0003430387 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI
    • Showalter R.E. Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. Mathematical Surveys and Monographs vol. 49 (1997), American Mathematical Society, Providence, RI
    • (1997) Mathematical Surveys and Monographs , vol.49
    • Showalter, R.E.1
  • 21
    • 4344654674 scopus 로고    scopus 로고
    • Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions
    • Wu H., and Zheng S. Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions. J. Differential Equations 204 (2004) 511-531
    • (2004) J. Differential Equations , vol.204 , pp. 511-531
    • Wu, H.1    Zheng, S.2
  • 22
    • 0003678750 scopus 로고
    • Springer-Verlag, New York Linear monotone operators, Translated from the German by the author and Leo F. Boron
    • Zeidler E. Nonlinear Functional Analysis and its Applications. II/A (1990), Springer-Verlag, New York Linear monotone operators, Translated from the German by the author and Leo F. Boron
    • (1990) Nonlinear Functional Analysis and its Applications. II/A
    • Zeidler, E.1


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