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Volumn 192, Issue 3-4, 2004, Pages 279-307

Universal attractor for some singular phase transition systems

Author keywords

Dissipativity; Heat flux law; Penrose Fife model; Phase transition; Universal attractor

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINT THEORY; GRAPH THEORY; MASS TRANSFER; MATHEMATICAL MODELS; PARAMETER ESTIMATION; THERMAL DIFFUSION; THERMAL EFFECTS;

EID: 2342628556     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.01.024     Document Type: Article
Times cited : (48)

References (25)
  • 1
    • 0000223804 scopus 로고
    • Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert
    • Baiocchi C., Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert. Ann. Mat. Pura Appl. IV. 76:1967;233-304.
    • (1967) Ann. Mat. Pura Appl. IV , vol.76 , pp. 233-304
    • Baiocchi, C.1
  • 2
    • 0001355254 scopus 로고
    • Inertial manifolds and inertial sets for the phase-field equations
    • Bates P.W., Zheng S., Inertial manifolds and inertial sets for the phase-field equations. J. Dyn. Diff. Eqs. 4:1992;375-398.
    • (1992) J. Dyn. Diff. Eqs. , vol.4 , pp. 375-398
    • Bates, P.W.1    Zheng, S.2
  • 3
    • 0007228960 scopus 로고
    • Universal attractor and inertial sets for the phase field model
    • Brochet D., Hilhorst D., Universal attractor and inertial sets for the phase field model. Appl. Math. Lett. 4:1991;59-62.
    • (1991) Appl. Math. Lett. , vol.4 , pp. 59-62
    • Brochet, D.1    Hilhorst, D.2
  • 4
    • 84894586322 scopus 로고    scopus 로고
    • Maximal attractor and inertial sets for a conserved phase field model
    • Brochet D., Hilhorst D., Novick-Cohen A., Maximal attractor and inertial sets for a conserved phase field model. Adv. Diff. Eqs. 1:1996;547-578.
    • (1996) Adv. Diff. Eqs. , vol.1 , pp. 547-578
    • Brochet, D.1    Hilhorst, D.2    Novick-Cohen, A.3
  • 5
    • 0003282411 scopus 로고
    • Opérateurs Maximaux Monotones et Sémi-groupes de Contractions dans les Espaces de Hilbert
    • North-Holland, Amsterdam
    • H. Brezis, Opérateurs Maximaux Monotones et Sémi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Mathematical Studies, vol. 5, North-Holland, Amsterdam, 1973.
    • (1973) North-Holland Mathematical Studies , vol.5
    • Brezis, H.1
  • 7
    • 0001133704 scopus 로고    scopus 로고
    • Weak solutions to the Penrose-Fife phase field model for a class of admissible heat flux laws
    • Colli P., Laurençot Ph., Weak solutions to the Penrose-Fife phase field model for a class of admissible heat flux laws. Physica D. 111:1998;311-334.
    • (1998) Physica D , vol.111 , pp. 311-334
    • Colli, P.1    Laurençot, Ph.2
  • 8
    • 34250131162 scopus 로고
    • An analysis of a phase field model of a free boundary
    • Caginalp G., An analysis of a phase field model of a free boundary. Arch. Rat. Mech. Anal. 92:1986;205-245.
    • (1986) Arch. Rat. Mech. Anal. , vol.92 , pp. 205-245
    • Caginalp, G.1
  • 9
    • 0013061246 scopus 로고    scopus 로고
    • Global solution to the Penrose-Fife phase field model with special heat flux law
    • Variation of Domains and Free-boundary Problems in Solid Mechanics (Paris, 1997), Kluwer Academic Publishers, Dordrecht
    • P. Colli, Ph. Laurençot, J. Sprekels, Global solution to the Penrose-Fife phase field model with special heat flux law, in: Variation of Domains and Free-boundary Problems in Solid Mechanics (Paris, 1997), Solid Mechanics and Application, vol. 66, Kluwer Academic Publishers, Dordrecht, 1999, pp. 181-188.
    • (1999) Solid Mechanics and Application , vol.66 , pp. 181-188
    • Colli, P.1    Laurençot, Ph.2    Sprekels, J.3
  • 10
    • 0000154802 scopus 로고    scopus 로고
    • Uniform attractors for a phase-field model with memory and quadratic nonlinearity
    • Giorgi C., Grasselli M., Pata V., Uniform attractors for a phase-field model with memory and quadratic nonlinearity. Indiana Univ. Math. J. 48:1999;1395-1445.
    • (1999) Indiana Univ. Math. J. , vol.48 , pp. 1395-1445
    • Giorgi, C.1    Grasselli, M.2    Pata, V.3
  • 11
    • 0035625134 scopus 로고    scopus 로고
    • Well-posedness and longtime behavior of the phase-field model with memory in a history space setting
    • Giorgi C., Grasselli M., Pata V., Well-posedness and longtime behavior of the phase-field model with memory in a history space setting. Quart. Appl. Math. 59:2001;701-736.
    • (2001) Quart. Appl. Math. , vol.59 , pp. 701-736
    • Giorgi, C.1    Grasselli, M.2    Pata, V.3
  • 12
    • 2342517967 scopus 로고    scopus 로고
    • Existence of a universal attractor for a parabolic-hyperbolic phase-field system
    • M. Grasselli, V. Pata, Existence of a universal attractor for a parabolic-hyperbolic phase-field system, Adv. Math. Sci. Appl. 13 (2003) 443-459.
    • (2003) Adv. Math. Sci. Appl. , vol.13 , pp. 443-459
    • Grasselli, M.1    Pata, V.2
  • 13
    • 0004136650 scopus 로고    scopus 로고
    • Inertial set for a phase transition model of Penrose-Fife type
    • correction: Adv. Math. Sci. Appl. 11 (2001) 481
    • A. Ito, N. Kenmochi, Inertial set for a phase transition model of Penrose-Fife type, Adv. Math. Sci. Appl. 10 (2000) 353-374; correction: Adv. Math. Sci. Appl. 11 (2001) 481.
    • (2000) Adv. Math. Sci. Appl. , vol.10 , pp. 353-374
    • Ito, A.1    Kenmochi, N.2
  • 14
    • 0000823389 scopus 로고    scopus 로고
    • Weak solutions of nonlinear systems for non-isothermal phase transitions
    • Kenmochi N., Kubo M., Weak solutions of nonlinear systems for non-isothermal phase transitions. Adv. Math. Sci. Appl. 9:1999;499-521.
    • (1999) Adv. Math. Sci. Appl. , vol.9 , pp. 499-521
    • Kenmochi, N.1    Kubo, M.2
  • 15
    • 0347556781 scopus 로고
    • Subdifferential operator approach to the Cahn-Hilliard equation with constraint
    • Kenmochi N., Niezgódka M., Pawlow I., Subdifferential operator approach to the Cahn-Hilliard equation with constraint. J. Diff. Eqs. 117:1995;320-356.
    • (1995) J. Diff. Eqs. , vol.117 , pp. 320-356
    • Kenmochi, N.1    Niezgódka, M.2    Pawlow, I.3
  • 16
    • 0001698023 scopus 로고
    • Solutions to a Penrose-Fife model of phase-field type
    • Laurençot Ph., Solutions to a Penrose-Fife model of phase-field type. J. Math. Anal. Appl. 185:1994;262-274.
    • (1994) J. Math. Anal. Appl. , vol.185 , pp. 262-274
    • Laurençot, Ph.1
  • 17
    • 21344432750 scopus 로고    scopus 로고
    • Long-time behaviour for a model of phase-field type
    • Laurençot Ph., Long-time behaviour for a model of phase-field type. Proc. R. Soc. Edinburgh, Sect. A. 126:1996;167-185.
    • (1996) Proc. R. Soc. Edinburgh, Sect. A , vol.126 , pp. 167-185
    • Laurençot, Ph.1
  • 20
    • 45149136070 scopus 로고
    • Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
    • Penrose O., Fife P.C., Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Physica D. 43:1990;44-62.
    • (1990) Physica D , vol.43 , pp. 44-62
    • Penrose, O.1    Fife, P.C.2
  • 21
    • 0000358571 scopus 로고
    • On the relation between the standard phase-field model and a "thermodynamically consistent" phase-field model
    • Penrose O., Fife P.C., On the relation between the standard phase-field model and a "thermodynamically consistent" phase-field model. Physica D. 69:1993;107-113.
    • (1993) Physica D , vol.69 , pp. 107-113
    • Penrose, O.1    Fife, P.C.2
  • 22
    • 84875341040 scopus 로고    scopus 로고
    • The conserved Penrose-Fife phase field model with special heat flux laws and memory effects
    • Rocca E., The conserved Penrose-Fife phase field model with special heat flux laws and memory effects. J. Integral Eqs. Appl. 14:2002;425-466.
    • (2002) J. Integral Eqs. Appl. , vol.14 , pp. 425-466
    • Rocca, E.1
  • 23
    • 0036532634 scopus 로고    scopus 로고
    • Maximal attractor for the coupled Cahn-Hilliard equations
    • Shen W., Zheng S., Maximal attractor for the coupled Cahn-Hilliard equations. Nonlinear Anal. Ser. A: Theory Meth. 49:2002;21-34.
    • (2002) Nonlinear Anal. Ser. A: Theory Meth. , vol.49 , pp. 21-34
    • Shen, W.1    Zheng, S.2
  • 24
    • 31244437718 scopus 로고    scopus 로고
    • Maximal attractors for the phase-field equations of Penrose-Fife type
    • Shen W., Zheng S., Maximal attractors for the phase-field equations of Penrose-Fife type. Appl. Math. Lett. 15:2002;1019-1023.
    • (2002) Appl. Math. Lett. , vol.15 , pp. 1019-1023
    • Shen, W.1    Zheng, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.