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Volumn 20, Issue 3-4, 1999, Pages 241-261

Some asymptotic analysis for hyperbolic relaxed Stefan problems with memory 1

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICS; ENERGY BALANCE EQUATIONS; EXISTENCE AND UNIQUENESS; HYPERBOLIC TYPE; LIMITING CASE; PHASE FIELDS; STEFAN PROBLEM; TRANSITION PROBLEMS;

EID: 0042043216     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (1)

References (41)
  • 1
    • 0002019044 scopus 로고    scopus 로고
    • Existence and asymptotic results for a system of integro-partial differential equations
    • S. Aizicovici and V. Barbu, Existence and asymptotic results for a system of integro-partial differential equations, Nonlinear Differential Equations Appl. 3 (1996), 1-18.
    • (1996) Nonlinear Differential Equations Appl. , vol.3 , pp. 1-18
    • Aizicovici, S.1    Barbu, V.2
  • 2
    • 0010659807 scopus 로고
    • Soluzioni ordinarie e generalizzate del problema di cauchy per equazioni differenziali astratte lineari del secondo ordine in spazi di Hilbert
    • C. Baiocchi, Soluzioni ordinarie e generalizzate del problema di Cauchy per equazioni differenziali astratte lineari del secondo ordine in spazi di Hilbert, Ricerche Mat. 16 (1967), 27-95.
    • (1967) Ricerche Mat. , vol.16 , pp. 27-95
    • Baiocchi, C.1
  • 3
    • 0000223804 scopus 로고
    • Sulle equazioni differenziali astratte del primo e del secondo ordine negli spazi di Hilbert
    • C. Baiocchi, Sulle equazioni differenziali astratte del primo e del secondo ordine negli spazi di Hilbert, Ann. Mat. Pura Appl. (4) 76 (1967), 233-304.
    • (1967) Ann. Mat. Pura Appl. , vol.76 , Issue.4 , pp. 233-304
    • Baiocchi, C.1
  • 6
    • 0032142504 scopus 로고    scopus 로고
    • Regularity and convergence results for a phase-field model with memory
    • G. Bonfanti and F. Luterotti, Regularity and convergence results for a phase-field model with memory, Math. Methods Appl. Sci. 21 (1998), 1085-1105.
    • (1998) Math. Methods Appl. Sci. , vol.21 , pp. 1085-1105
    • Bonfanti, G.1    Luterotti, F.2
  • 7
    • 25444450783 scopus 로고    scopus 로고
    • Asymptotic analysis to a phase-field model with a nonsmooth memory kernel
    • to appear
    • G. Bonfanti and F. Luterotti, Asymptotic analysis to a phase-field model with a nonsmooth memory kernel, J. Convex Anal., to appear.
    • J. Convex Anal.
    • Bonfanti, G.1    Luterotti, F.2
  • 8
    • 84875341734 scopus 로고    scopus 로고
    • Global solution to a phase-field model with memory and quadratic nonlinearity
    • to appear
    • G. Bonfanti and F. Luterotti, Global solution to a phase-field model with memory and quadratic nonlinearity, Adv. Math. Sci. Appl., to appear
    • Adv. Math. Sci. Appl.
    • Bonfanti, G.1    Luterotti, F.2
  • 10
    • 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. 92 (1986), 205-245.
    • (1986) Arch. Rational Mech. Anal. , vol.92 , pp. 205-245
    • Caginalp, G.1
  • 12
    • 84973509052 scopus 로고
    • Thermoelasticity with second sound: A review
    • D.S. Chandrasekharaiah, Thermoelasticity with second sound: a review, Appl. Mech. Rev. 39 (1986), 355-376.
    • (1986) Appl. Mech. Rev. , vol.39 , pp. 355-376
    • Chandrasekharaiah, D.S.1
  • 13
    • 0007080113 scopus 로고    scopus 로고
    • Positive kernel and zero time relaxation in a phase field model with memory
    • L. Chiusano and P. Colli, Positive kernel and zero time relaxation in a phase field model with memory, Comm. Appl. Anal. 2 (1998), 531-550.
    • (1998) Comm. Appl. Anal. , vol.2 , pp. 531-550
    • Chiusano, L.1    Colli, P.2
  • 15
    • 0000522482 scopus 로고
    • Equipresence and constitutive equations for rigid heat conductors
    • D. Coleman and 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, D.1    Gurtin, M.E.2
  • 16
    • 0007091804 scopus 로고    scopus 로고
    • Convergence of phase field to phase relaxation models with memory
    • P. Colli, G. Gilardi and M. Grasselli, Convergence of phase field to phase relaxation models with memory, Ann. Univ. Ferrara Sez. VII (N.S.) 41(Suppl.) (1996), 1-14.
    • (1996) Ann. Univ. Ferrara Sez. VII (N.S.) , vol.41 , Issue.SUPPL. , pp. 1-14
    • Colli, P.1    Gilardi, G.2    Grasselli, M.3
  • 17
    • 0000361536 scopus 로고    scopus 로고
    • Global smooth solution to the standard phase-field model with memory
    • P. Colli, G. Gilardi and M. Grasselli, Global smooth solution to the standard phase-field model with memory, Adv. Differential Equations 2 (1997), 453-486.
    • (1997) Adv. Differential Equations , vol.2 , pp. 453-486
    • Colli, P.1    Gilardi, G.2    Grasselli, M.3
  • 19
    • 0000361534 scopus 로고    scopus 로고
    • Well-posedness of the weak formulation for the phase-field model with memory
    • P. Colli, G. Gilardi and M. Grasselli, Well-posedness of the weak formulation for the phase-field model with memory, Adv. Differential Equations 2 (1997), 487-508.
    • (1997) Adv. Differential Equations , vol.2 , pp. 487-508
    • Colli, P.1    Gilardi, G.2    Grasselli, M.3
  • 20
    • 0007132105 scopus 로고    scopus 로고
    • Asymptotic analysis of a phase-field model with memory for vanishing time relaxation
    • P. Colli, G. Gilardi and M. Grasselli, Asymptotic analysis of a phase-field model with memory for vanishing time relaxation, Hiroshima Math. J. 29 (1999), 117-143.
    • (1999) Hiroshima Math. J. , vol.29 , pp. 117-143
    • Colli, P.1    Gilardi, G.2    Grasselli, M.3
  • 22
    • 0042437935 scopus 로고
    • An existence result for a hyperbolic phase transition problem with memory
    • P. Colli and M. Grasselli, An existence result for a hyperbolic phase transition problem with memory, Appl. Math. Lett. 5 (1992), 99-102.
    • (1992) Appl. Math. Lett. , vol.5 , pp. 99-102
    • Colli, P.1    Grasselli, M.2
  • 23
    • 0042938651 scopus 로고
    • Hyperbolic phase change problems in materials with memory
    • P. Colli and M. Grasselli, Hyperbolic phase change problems in materials with memory, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 571-592.
    • (1993) Proc. Roy. Soc. Edinburgh Sect. A , vol.123 , pp. 571-592
    • Colli, P.1    Grasselli, M.2
  • 24
    • 0001141782 scopus 로고
    • Justification of a hyperbolic approach to phase change in materials with memory
    • P. Colli and M. Grasselli, Justification of a hyperbolic approach to phase change in materials with memory, Asympt. Anal. 10 (1995), 303-304.
    • (1995) Asympt. Anal. , vol.10 , pp. 303-304
    • Colli, P.1    Grasselli, M.2
  • 25
    • 0042938643 scopus 로고    scopus 로고
    • Convergence of parabolic to hyperbolic phase change models with memory
    • P. Colli and M. Grasselli, Convergence of parabolic to hyperbolic phase change models with memory, Adv. Math. Sci. Appl. 6 (1996), 147-176.
    • (1996) Adv. Math. Sci. Appl. , vol.6 , pp. 147-176
    • Colli, P.1    Grasselli, M.2
  • 26
    • 0000071731 scopus 로고    scopus 로고
    • Existence and stabilization of solutions to the phase-field model with memory
    • P. Colli and Ph. Laurençot, Existence and stabilization of solutions to the phase-field model with memory, J. Integral Equations Appl. 10 (1998), 169-194.
    • (1998) J. Integral Equations Appl. , vol.10 , pp. 169-194
    • Colli, P.1    Laurençot, Ph.2
  • 27
    • 0001649845 scopus 로고    scopus 로고
    • Uniqueness of weak solutions to the phase-field model with memory
    • P. Colli and Ph. Laurençot, 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
    • Colli, P.1    Laurençot, Ph.2
  • 28
    • 0000137841 scopus 로고
    • Subdifferential operator approach to a class of nonlinear systems for Stefan problems with phase relaxation
    • A. Damlamian, N. Kenmochi and N. Sato, Subdifferential operator approach to a class of nonlinear systems for Stefan problems with phase relaxation, Nonlinear Anal. 23 (1994), 115-142.
    • (1994) Nonlinear Anal. , vol.23 , pp. 115-142
    • Damlamian, A.1    Kenmochi, N.2    Sato, N.3
  • 29
    • 0001092522 scopus 로고    scopus 로고
    • Phase field models for free boundary problems
    • G.J. Fix, Phase field models for free boundary problems, in: Free Boundary Problems: Theory and Applications, Vol. II, A. Fasano and M. Primicerio, eds, Pitman Res. Notes Math. Ser., Vol. 79, Longman, London, 1983, pp. 580-589.
    • Free Boundary Problems: Theory and Applications , vol.2
    • Fix, G.J.1
  • 30
    • 0001092522 scopus 로고    scopus 로고
    • Longman, London
    • G.J. Fix, Phase field models for free boundary problems, in: Free Boundary Problems: Theory and Applications, Vol. II, A. Fasano and M. Primicerio, eds, Pitman Res. Notes Math. Ser., Vol. 79, Longman, London, 1983, pp. 580-589.
    • (1983) Pitman Res. Notes Math. Ser. , vol.79 , pp. 580-589
    • Fasano, A.1    Primicerio, M.2
  • 32
    • 0042437933 scopus 로고
    • The Stefan problem for a hyperbolic heat equation
    • A. Friedman and B. Hu, The Stefan problem for a hyperbolic heat equation, J. Math. Anal. Appl. 138 (1989), 249-279.
    • (1989) J. Math. Anal. Appl. , vol.138 , pp. 249-279
    • Friedman, A.1    Hu, B.2
  • 33
    • 34250511985 scopus 로고
    • A general theory of heat conduction with finite wave speeds
    • M.E. Gurtin and 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
  • 35
    • 35949014378 scopus 로고
    • Addendum to the paper "Heat waves"
    • D.D. Joseph and L. Preziosi, Addendum to the paper "Heat waves" [Rev. Modern Phys. 61 (1989), 41-73], Rev. Modern Phys. 62 (1990), 375-391.
    • (1989) Rev. Modern Phys. , vol.61 , pp. 41-73
    • Joseph, D.D.1    Preziosi, L.2
  • 36
    • 0004135196 scopus 로고
    • D.D. Joseph and L. Preziosi, Addendum to the paper "Heat waves" [Rev. Modern Phys. 61 (1989), 41-73], Rev. Modern Phys. 62 (1990), 375-391.
    • (1990) Rev. Modern Phys. , vol.62 , pp. 375-391
  • 37
    • 21344432750 scopus 로고    scopus 로고
    • Long-time behaviour for a model of phase-field type
    • Ph. 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, Ph.1
  • 38
    • 0041435531 scopus 로고
    • The well-posedness of a hyperbolic Stefan problem
    • D. Li, The well-posedness of a hyperbolic Stefan problem, Quart. Appl. Math. 45 (1989), 221-231.
    • (1989) Quart. Appl. Math. , vol.45 , pp. 221-231
    • Li, D.1
  • 41
    • 0001123368 scopus 로고
    • Stefan problem with phase relaxation
    • A. Visintin, Stefan problem with phase relaxation, IMA J. Appl. Math. 34 (1985), 225-245.
    • (1985) IMA J. Appl. Math. , vol.34 , pp. 225-245
    • Visintin, A.1


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