메뉴 건너뛰기




Volumn 16, Issue 5, 2004, Pages 441-451

New models of Cahn-Hilliard-Gurtin equations

Author keywords

Cahn Hilliard equation; Constitutive equations; Dissipation inequality; Existence and uniqueness of solutions; Microforce balance; Second law of thermodynamics

Indexed keywords


EID: 3543039432     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-003-0169-6     Document Type: Article
Times cited : (9)

References (27)
  • 1
    • 43449102981 scopus 로고
    • On spinodal decomposition
    • Cahn, J.W.: On spinodal decomposition. Acta Metall. 9, 795-801 (1961)
    • (1961) Acta Metall. , vol.9 , pp. 795-801
    • Cahn, J.W.1
  • 2
    • 0346310165 scopus 로고
    • The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
    • Translation of J.D. van der Waals'
    • Rowlinson, J.S.: Translation of J.D. van der Waals' "The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density". J. Stat. Phys. 20(2), 197-244 (1979)
    • (1979) J. Stat. Phys. , vol.20 , Issue.2 , pp. 197-244
    • Rowlinson, J.S.1
  • 4
    • 0031116136 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interaction I. Macroscopic limits
    • Giacomin, G., Lebowitz, J.L.: Phase segregation dynamics in particle systems with long range interaction I. Macroscopic limits. J. Stat. Phys. 87(1-2), 37-61 (1997)
    • (1997) J. Stat. Phys. , vol.87 , Issue.1-2 , pp. 37-61
    • Giacomin, G.1    Lebowitz, J.L.2
  • 5
    • 0032291814 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interaction II. Interface motion
    • Giacomin, G., Lebowitz, J.L.: Phase segregation dynamics in particle systems with long range interaction II. Interface motion. SIAM J. Appl. Math. 58, 1707-1729 (1998)
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1707-1729
    • Giacomin, G.1    Lebowitz, J.L.2
  • 6
    • 0001158204 scopus 로고    scopus 로고
    • Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
    • Gurtin, M.: Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92, 178-192 (1996)
    • (1996) Physica D , vol.92 , pp. 178-192
    • Gurtin, M.1
  • 7
    • 0000063685 scopus 로고
    • Continuum theory of thermally induced phase transitions based on an order parameter
    • Fried, E., Gurtin, M.: Continuum theory of thermally induced phase transitions based on an order parameter. Physica D 68, 326-343 (1993)
    • (1993) Physica D , vol.68 , pp. 326-343
    • Fried, E.1    Gurtin, M.2
  • 8
    • 26544469625 scopus 로고
    • Dynamic solid-solid phase transitions with phase characterized by an order parameter
    • Fried, E., Gurtin, M.: Dynamic solid-solid phase transitions with phase characterized by an order parameter. Physica D 72, 287-308 (1994)
    • (1994) Physica D , vol.72 , pp. 287-308
    • Fried, E.1    Gurtin, M.2
  • 9
    • 3543017185 scopus 로고    scopus 로고
    • PhD thesis, Université de Poitiers
    • Bonfoh, A.: PhD thesis, Université de Poitiers (2001)
    • (2001)
    • Bonfoh, A.1
  • 11
    • 0003314329 scopus 로고    scopus 로고
    • Generalized Cahn-Hilliard equations with a logarithmic free energy
    • Cherfils, L., Miranville, A.: Generalized Cahn-Hilliard equations with a logarithmic free energy. Rev. Real Acad. Ciencias 94(1), 19-32 (2000)
    • (2000) Rev. Real Acad. Ciencias , vol.94 , Issue.1 , pp. 19-32
    • Cherfils, L.1    Miranville, A.2
  • 12
    • 1642391961 scopus 로고    scopus 로고
    • The finite dimensional attractor for a 4th order system of the Cahn-Hilliard type with a supercritical nonlinearity
    • Efendiev, M., Gajewski, H., Zelik, S.: The finite dimensional attractor for a 4th order system of the Cahn-Hilliard type with a supercritical nonlinearity. Adv. Diff. Equ. 7(9), 1073-1100 (2002)
    • (2002) Adv. Diff. Equ. , vol.7 , Issue.9 , pp. 1073-1100
    • Efendiev, M.1    Gajewski, H.2    Zelik, S.3
  • 13
    • 0001044039 scopus 로고    scopus 로고
    • Some generalizations of the Cahn-Hilliard equation
    • Miranville, A.: Some generalizations of the Cahn-Hilliard equation. Asymptotic Anal. 22, 235-259 (2000)
    • (2000) Asymptotic Anal. , vol.22 , pp. 235-259
    • Miranville, A.1
  • 14
    • 0035457838 scopus 로고    scopus 로고
    • Long-time behavior of some models of Cahn-Hilliard equations in deformable continua
    • Miranville, A.: Long-time behavior of some models of Cahn-Hilliard equations in deformable continua. Nonlinear Anal. Ser. B 2(3), 273-304 (2001)
    • (2001) Nonlinear Anal. Ser. B , vol.2 , Issue.3 , pp. 273-304
    • Miranville, A.1
  • 15
    • 0000161026 scopus 로고    scopus 로고
    • Dynamical aspect of a generalized Cahn-Hilliard equation based on a microforce balance
    • Piétrus, A., Miranville, A., Rakotoson, J.-M.: Dynamical aspect of a generalized Cahn-Hilliard equation based on a microforce balance. Asymptotic Anal. 16, 315-345 (1998)
    • (1998) Asymptotic Anal. , vol.16 , pp. 315-345
    • Piétrus, A.1    Miranville, A.2    Rakotoson, J.-M.3
  • 16
    • 84880179958 scopus 로고    scopus 로고
    • New generalizations of the Cahn-Hilliard equation based on a microforce balance
    • Wendland, W., Efendiev, M. (eds) (Lecture Notes in Applied and Computational Mechanics), Springer Berlin Heidelberg New York
    • Efendiev, M., Miranville, A.: New generalizations of the Cahn-Hilliard equation based on a microforce balance. In: Wendland, W., Efendiev, M. (eds) Analysis and Simulation of Multifield Problems (Lecture Notes in Applied and Computational Mechanics), Springer Berlin Heidelberg New York (2003)
    • (2003) Analysis and Simulation of Multifield Problems
    • Efendiev, M.1    Miranville, A.2
  • 17
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system I. Interfacial free energy
    • Cahn, J.W., Hilliard, J.E.: Free energy of a nonuniform system I. Interfacial free energy. J. Chem. Phys. 2, 258-267 (1958)
    • (1958) J. Chem. Phys. , vol.2 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 18
    • 21844484383 scopus 로고
    • An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy
    • Barrett, J.W., Blowey, J.F.: An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy. Numer. Math. 72, 1-20 (1995)
    • (1995) Numer. Math. , vol.72 , pp. 1-20
    • Barrett, J.W.1    Blowey, J.F.2
  • 19
    • 21144473934 scopus 로고
    • Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
    • Copetti, M.I.M., Elliott, C.M.: Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Numer. Math. 63, 39-65 (1992)
    • (1992) Numer. Math. , vol.63 , pp. 39-65
    • Copetti, M.I.M.1    Elliott, C.M.2
  • 20
    • 0029307671 scopus 로고
    • On the Cahn-Hilliard equation with a logarithmic free energy
    • Debussche, A., Dettori, L.: On the Cahn-Hilliard equation with a logarithmic free energy. Nonlinear Anal. TMA 24, 1491-1514 (1995)
    • (1995) Nonlinear Anal. TMA , vol.24 , pp. 1491-1514
    • Debussche, A.1    Dettori, L.2
  • 21
    • 0030526461 scopus 로고    scopus 로고
    • On the Cahn-Hilliard equation with degenerate mobility
    • Elliott, C.M., Garcke, H.: On the Cahn-Hilliard equation with degenerate mobility. SIAM J. Math. Anal. 27(2), 404-423 (1996)
    • (1996) SIAM J. Math. Anal. , vol.27 , Issue.2 , pp. 404-423
    • Elliott, C.M.1    Garcke, H.2
  • 23
    • 3543003344 scopus 로고    scopus 로고
    • Robust exponential attractors for Cahn-Hilliard type equations with singular potentials
    • in press
    • Miranville, A., Zelik, S.: Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Math. Models Appl. Sci. (in press)
    • Math. Models Appl. Sci.
    • Miranville, A.1    Zelik, S.2
  • 25
    • 0035888218 scopus 로고    scopus 로고
    • Consistent models of Cahn-Hilliard-Gurtin equations with Neumann boundary conditions
    • Miranville, A.: Consistent models of Cahn-Hilliard-Gurtin equations with Neumann boundary conditions. Physica D 158(1-4), 233-257 (2001)
    • (2001) Physica D , vol.158 , Issue.1-4 , pp. 233-257
    • Miranville, A.1
  • 26
    • 0742276296 scopus 로고    scopus 로고
    • On a nonlocal model of non-isothermal phase separation
    • Gajewski, H.: On a nonlocal model of non-isothermal phase separation. Adv. Math. Sci. Appl. 12(2), 569-586 (2002)
    • (2002) Adv. Math. Sci. Appl. , vol.12 , Issue.2 , pp. 569-586
    • Gajewski, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.