메뉴 건너뛰기




Volumn 48, Issue 4, 1999, Pages 1395-1444

Uniform attractors for a phase-field model with memory and quadratic nonlinearity

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000154802     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1999.48.1793     Document Type: Article
Times cited : (79)

References (39)
  • 1
    • 0002019044 scopus 로고    scopus 로고
    • Existence and asymptotic results for a system of integro-partial differential equations
    • S. AIZICOVICI & V. BARBU, Existence and asymptotic results for a system of integro-partial differential equations, NoDEA Nonlinear Differential Equations Appl. 3 (1996), 1-18.
    • (1996) NoDEA Nonlinear Differential Equations Appl. , vol.3 , pp. 1-18
    • Aizicovici, S.1    Barbu, V.2
  • 4
    • 0000770831 scopus 로고    scopus 로고
    • Global solution to a phase-field model with memory and quadratic nonlinearity
    • G. BONFANTI & F. LUTEROTTI, Global solution to a phase-field model with memory and quadratic nonlinearity, Adv. Math. Sci. Appl. 9 (1999), 523-538.
    • (1999) Adv. Math. Sci. Appl. , vol.9 , pp. 523-538
    • Bonfanti, G.1    Luterotti, F.2
  • 5
    • 0032142504 scopus 로고    scopus 로고
    • Regularity and convergence results for a phase-field model with memory
    • _, Regularity and convergence results for a phase-field model with memory, Math. Meth. Appl. Sci. 21 (1998), 1085-1105.
    • (1998) Math. Meth. Appl. Sci. , vol.21 , pp. 1085-1105
  • 6
    • 0003282411 scopus 로고
    • Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
    • North-Holland, Amsterdam
    • H. BRÉZIS, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Math. Stud., vol. 5, North-Holland, Amsterdam, 1973.
    • (1973) North-holland Math. Stud. , vol.5
    • Brézis, H.1
  • 7
    • 0003353189 scopus 로고    scopus 로고
    • Hysteresis and phase transitions
    • Springer, New York
    • M. BROKATE & J. SPREKELS, Hysteresis and Phase Transitions, Coll. Appl. Math. Sci., vol. 121, Springer, New York, 1996.
    • (1996) Coll. Appl. Math. Sci. , vol.121
    • Brokate, M.1    Sprekels, J.2
  • 8
    • 34250131162 scopus 로고
    • An analysis of a phase field model of a free boundary
    • G. CAGINALP, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal. 96 (1985), 205-245.
    • (1985) Arch. Rational Mech. Anal. , vol.96 , pp. 205-245
    • Caginalp, G.1
  • 9
    • 0004152738 scopus 로고
    • Nonautonomous evolution equations and their attractors
    • V. V. CHEPYZHOV & M. I. VISHIK, Nonautonomous evolution equations and their attractors, Russian J. Math. Phys. 1 (1993), 165-190.
    • (1993) Russian J. Math. Phys. , vol.1 , pp. 165-190
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 10
    • 0001530660 scopus 로고
    • Attractors of non-autonomous dynamical systems and their dimension
    • _, Attractors of non-autonomous dynamical systems and their dimension, J. Math. Pures Appl. 73 (1994), 279-333.
    • (1994) J. Math. Pures Appl. , vol.73 , pp. 279-333
  • 11
    • 0000754878 scopus 로고
    • Non-autonomous evolutionary equations with translation compact symbols and their attractor
    • _, Non-autonomous evolutionary equations with translation compact symbols and their attractor, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), 153-158.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.321 , pp. 153-158
  • 12
    • 0000522482 scopus 로고
    • Equipresence and constitutive equations for rigid heat conductors
    • B. D. COLEMAN & M. E. GURTIN, Equipresence and constitutive equations for rigid heat conductors, Z. Angew. Math. Phys. 18 (1967), 199-208.
    • (1967) Z. Angew. Math. Phys. , vol.18 , pp. 199-208
    • Coleman, B.D.1    Gurtin, M.E.2
  • 13
    • 0000071731 scopus 로고    scopus 로고
    • Existence and stabilization of solutions to the phase- field model with memory
    • P. COLLI & PH. LAURENÇOT, Existence and stabilization of solutions to the phase- field model with memory, J. Integral Equations Appl. 10 (1998), 168-194.
    • (1998) J. Integral Equations Appl. , vol.10 , pp. 168-194
    • Colli, P.1    Laurençot, Ph.2
  • 14
    • 0001649845 scopus 로고    scopus 로고
    • Uniqueness of weak solutions to the phase-field model with memory
    • _, Uniqueness of weak solutions to the phase-field model with memory, J. Math. Sci. Univ. Tokyo 5 (1998), 459-476.
    • (1998) J. Math. Sci. Univ. Tokyo , vol.5 , pp. 459-476
  • 15
    • 0000361536 scopus 로고    scopus 로고
    • Global smooth solution to the standard phase-field model with memory
    • P. COLLI, G. GILARDI & M. GRASSELLI, Global smooth solution to the standard phase-field model with memory, Adv. Differential Equations 3 (1997), 453-486.
    • (1997) Adv. Differential Equations , vol.3 , pp. 453-486
    • Colli, P.1    Gilardi, G.2    Grasselli, M.3
  • 16
    • 0000361534 scopus 로고    scopus 로고
    • Well-posedness of the weak formulation for the phase-field model with memory
    • _, Well-posedness of the weak formulation for the phase-field model with memory, Adv. Differential Equations 3 (1997), 487-508.
    • (1997) Adv. Differential Equations , vol.3 , pp. 487-508
  • 17
    • 0007091804 scopus 로고    scopus 로고
    • Convergence of phase field to phase relaxation models with memory
    • _, Convergence of phase field to phase relaxation models with memory, Ann. Univ. Ferrara Ser. VII (N.S.), Suppl. 41 (1996), 1-14.
    • (1996) Ann. Univ. Ferrara Ser. VII (N.S.), Suppl. , vol.41 , pp. 1-14
  • 18
    • 0007078291 scopus 로고    scopus 로고
    • Asymptotic justification of the phase-field model with memory
    • _, Asymptotic justification of the phase-field model with memory, Comm. Appl. Nonlinear Anal. 6 (1999), 1-27.
    • (1999) Comm. Appl. Nonlinear Anal. , vol.6 , pp. 1-27
  • 21
    • 0001629395 scopus 로고
    • Asymptotic stability in viscoelasticity
    • C. M. DAFERMOS, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. 37 (1970), 297-308.
    • (1970) Arch. Rational Mech. Anal. , vol.37 , pp. 297-308
    • Dafermos, C.M.1
  • 22
    • 0000063685 scopus 로고
    • Continuum theory of thermally induced phase transition based on an order parameter
    • E. FRIED & M. E. GURTIN, Continuum theory of thermally induced phase transition based on an order parameter, Physica D 68 (1993), 326-343.
    • (1993) Physica D , vol.68 , pp. 326-343
    • Fried, E.1    Gurtin, M.E.2
  • 25
    • 84875104886 scopus 로고    scopus 로고
    • Uniform attractors for a non-autonomous semilinear heat equation with memory
    • to appear
    • _, Uniform attractors for a non-autonomous semilinear heat equation with memory, to appear, Quart. Appl. Math.
    • Quart. Appl. Math.
  • 26
    • 0032361134 scopus 로고    scopus 로고
    • Longtime behavior of a homogenized model in viscoelastodynamics
    • M. GRASSELLI & V. PATA, Longtime behavior of a homogenized model in viscoelastodynamics, Discrete Contin. Dynam. Systems 4 (1998), 339-358.
    • (1998) Discrete Contin. Dynam. Systems , vol.4 , pp. 339-358
    • Grasselli, M.1    Pata, V.2
  • 27
    • 34250511985 scopus 로고
    • A general theory of heat conduction with finite wave speeds
    • M. E. GURTIN & A. C. PIPKIN, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31 (1968), 113-126.
    • (1968) Arch. Rational Mech. Anal. , vol.31 , pp. 113-126
    • Gurtin, M.E.1    Pipkin, A.C.2
  • 28
    • 4244114580 scopus 로고
    • Renormalization-group methods for critical dynamics: I. Recursion relations and effects of energy conservation
    • B. I. HALPERIN, P. C. HOHENBERG & S. K. MA, Renormalization-group methods for critical dynamics: I. Recursion relations and effects of energy conservation, Phys. Rev. B 10 (1974), 139-153.
    • (1974) Phys. Rev. B , vol.10 , pp. 139-153
    • Halperin, B.I.1    Hohenberg, P.C.2    Ma, S.K.3
  • 30
    • 0040108624 scopus 로고    scopus 로고
    • Attractors of semigroups associated with nonlinear systems for diffusive phase separation
    • N. KENMOCHI, Attractors of semigroups associated with nonlinear systems for diffusive phase separation, Abstr. Appl. Anal. 1 (1996), 169-192.
    • (1996) Abstr. Appl. Anal. , vol.1 , pp. 169-192
    • Kenmochi, N.1
  • 31
    • 0038924464 scopus 로고    scopus 로고
    • Global attractor of the semigroup associated to a phase-field model with constraint
    • Pitman Res. Notes Math. Ser., Longman, Harlow
    • _, Global attractor of the semigroup associated to a phase-field model with constraint, Free Boundary Problems, Theory and Applications (Zakopane, 1995), vol. 363, Pitman Res. Notes Math. Ser., Longman, Harlow, 1996, pp. 111-125.
    • (1996) Free Boundary Problems, Theory and Applications (Zakopane, 1995) , vol.363 , pp. 111-125
  • 32
    • 84875084822 scopus 로고
    • Global attractor of the semigroup of a non-isothermal model for phase separation
    • Curvature Flows and Related Topics (Levico, 1994), Gakkotosho, Tokyo
    • N. KENMOCHI, M. NIEZGÓDKA & S. M. ZHENG, Global attractor of the semigroup of a non-isothermal model for phase separation, Curvature Flows and Related Topics (Levico, 1994), Gakuto Internat. Ser. Math. Sci. Appl. 5, Gakkotosho, Tokyo, 1995, pp. 129-143.
    • (1995) Gakuto Internat. Ser. Math. Sci. Appl. , vol.5 , pp. 129-143
    • Kenmochi, N.1    Niezgódka, M.2    Zheng, S.M.3
  • 33
    • 21344432750 scopus 로고    scopus 로고
    • Long-time behaviour for a model of phase-field type
    • P. LAURENÇOT, Long-time behaviour for a model of phase-field type, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 167-185.
    • (1996) Proc. Roy. Soc. Edinburgh Sect. A , vol.126 , pp. 167-185
    • Laurençot, P.1
  • 34
    • 0001410999 scopus 로고    scopus 로고
    • Traveling waves of dissipative non-autonomous hyperbolic equations in a strip
    • V. PATA, G. PROUSE & M. I. VISHIK, Traveling waves of dissipative non-autonomous hyperbolic equations in a strip, Adv. Differential Equations 3 (1998), 249-270.
    • (1998) Adv. Differential Equations , vol.3 , pp. 249-270
    • Pata, V.1    Prouse, G.2    Vishik, M.I.3
  • 36
    • 45149136070 scopus 로고
    • Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
    • O. PENROSE & P. C. FIFE, 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
  • 37
    • 0032188508 scopus 로고    scopus 로고
    • Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys
    • J. SPREKELS & S. ZHENG, Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys, Physica D 121 (1998), 252-262.
    • (1998) Physica D , vol.121 , pp. 252-262
    • Sprekels, J.1    Zheng, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.