메뉴 건너뛰기




Volumn 4, Issue 1, 2005, Pages 115-142

Trajectory and global attractors of dissipative hyperbolic equations with memory

Author keywords

Dissipative hyperbolic equation; Emory kernel; Trajectory attractor

Indexed keywords


EID: 27644502038     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2005.4.115     Document Type: Article
Times cited : (20)

References (31)
  • 1
    • 0000154802 scopus 로고    scopus 로고
    • Uniform attractors for a phase-field model with memory and quadratic nonlinearity
    • C. Giorgi, M. Grasselli and V. Pata, Uniform attractors for a phase-field model with memory and quadratic nonlinearity, Indiana Univ. Math. J., (4) 48 (1999), 1395-1445.
    • (1999) Indiana Univ. Math. J. , vol.48 , Issue.4 , pp. 1395-1445
    • Giorgi, C.1    Grasselli, M.2    Pata, V.3
  • 2
    • 0035625134 scopus 로고    scopus 로고
    • Well-posedness and longtime behavior of the phase-field model with memory in a history space setting
    • C. Giorgi, M. Grasselli and V. Pata, Well-posedness and longtime behavior of the phase-field model with memory in a history space setting, Quart. Appl. Math., (4) 59 (2001), 701-736.
    • (2001) Quart. Appl. Math. , vol.59 , Issue.4 , pp. 701-736
    • Giorgi, C.1    Grasselli, M.2    Pata, V.3
  • 3
    • 0038116280 scopus 로고    scopus 로고
    • Upper semicontinuous attractor for a hyperbolic phase-field model with memory
    • M. Grasselli and V. Pata, Upper semicontinuous attractor for a hyperbolic phase-field model with memory, Indiana Univ. Math. J., (3) 50 (2001), 1281-1308.
    • (2001) Indiana Univ. Math. J. , vol.50 , Issue.3 , pp. 1281-1308
    • Grasselli, M.1    Pata, V.2
  • 4
    • 0842283817 scopus 로고    scopus 로고
    • Uniform attractors of nonautonomous dynamical systems with memory
    • Evolution equations, semigroups and functional analysis (Milano, 2000), Basel, Birkhäuser
    • M. Grasselli and V. Pata, Uniform attractors of nonautonomous dynamical systems with memory, Evolution equations, semigroups and functional analysis (Milano, 2000), 155-178, Progr. Nonlin. Diff. Eq. Appl., 50, Basel, Birkhäuser, 2002.
    • (2002) Progr. Nonlin. Diff. Eq. Appl. , vol.50 , pp. 155-178
    • Grasselli, M.1    Pata, V.2
  • 5
    • 0035311870 scopus 로고    scopus 로고
    • Global attractors for degenerate partial differential equations from nonlinear viscoelasticity
    • J.P. Wilber and S.S. Antman, Global attractors for degenerate partial differential equations from nonlinear viscoelasticity, Phys. D, (3-4) 150 (2001), 177-206.
    • (2001) Phys. D , vol.150 , Issue.3-4 , pp. 177-206
    • Wilber, J.P.1    Antman, S.S.2
  • 6
    • 0037366232 scopus 로고    scopus 로고
    • Global attractor for damped semilinear elastic beam equations with memory
    • A. Marzocchi and E. Vuk, Global attractor for damped semilinear elastic beam equations with memory, Z. Angew. Math. Phys., (2) 54 (2003), 224-234.
    • (2003) Z. Angew. Math. Phys. , vol.54 , Issue.2 , pp. 224-234
    • Marzocchi, A.1    Vuk, E.2
  • 7
    • 0002693827 scopus 로고    scopus 로고
    • Asymptotic behavior of a semilinear problem in heat conduction with memory
    • C. Giorgi, V. Pata and A. Marzocchi, Asymptotic behavior of a semilinear problem in heat conduction with memory, Nonlin. Diff. Eq. Appl. (NoDEA), (3) 5 (1998), 333-354.
    • (1998) Nonlin. Diff. Eq. Appl. (NoDEA) , vol.5 , Issue.3 , pp. 333-354
    • Giorgi, C.1    Pata, V.2    Marzocchi, A.3
  • 8
    • 0034541102 scopus 로고    scopus 로고
    • Uniform extractors for a non-utonomous semtimear heat equation with memory
    • C. Giorgi, V. Pata and A. Marzocchi, Uniform extractors for a non-utonomous semtimear heat equation with memory, Quart. Appl. Math., (4) 58 (2000), 661-683.
    • (2000) Quart. Appl. Math. , vol.58 , Issue.4 , pp. 661-683
    • Giorgi, C.1    Pata, V.2    Marzocchi, A.3
  • 9
    • 0008329457 scopus 로고    scopus 로고
    • Exponential stability in linear heat conduction with memory: A semigroup approach
    • C. Giorgi, M.G. Naso and V. Pata, Exponential stability in linear heat conduction with memory: a semigroup approach, Comm. Appl. Anal., (1) 5 (2001), 121-133.
    • (2001) Comm. Appl. Anal. , vol.5 , Issue.1 , pp. 121-133
    • Giorgi, C.1    Naso, M.G.2    Pata, V.3
  • 10
    • 23044528304 scopus 로고    scopus 로고
    • Hyperbolic limit of parabolic semilinear heat equations with fading memory
    • V. Pata, Hyperbolic limit of parabolic semilinear heat equations with fading memory, Z. Anal. Anwendungen, (2) 20 (2001), 359-377.
    • (2001) Z. Anal. Anwendungen , vol.20 , Issue.2 , pp. 359-377
    • Pata, V.1
  • 11
    • 0000035723 scopus 로고    scopus 로고
    • Asymptotic behavior of a nonlinear hyperbolic heat equation with memory
    • C. Giorgi and V. Pata, Asymptotic behavior of a nonlinear hyperbolic heat equation with memory, Nonlin. Diff. Eq. Appl. (NoDEA), (2) 8 (2001), 157-171.
    • (2001) Nonlin. Diff. Eq. Appl. (NoDEA) , vol.8 , Issue.2 , pp. 157-171
    • Giorgi, C.1    Pata, V.2
  • 12
    • 0001629395 scopus 로고
    • Asymptotic stability in viscoelasticity
    • C.M. Dafermos, Asymptotic stability in viscoelasticity, Arch, national Mech. Anal., 37 (1970), 297-308.
    • (1970) Arch, National Mech. Anal. , vol.37 , pp. 297-308
    • Dafermos, C.M.1
  • 13
    • 0003246899 scopus 로고    scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • Springer-Verlag, New York, 1988; 2nd ed.
    • R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematics Series, 68, Springer-Verlag, New York, 1988; 2nd ed. 1997.
    • (1997) Applied Mathematics Series , vol.68
    • Temam, R.1
  • 15
    • 0003293929 scopus 로고
    • Asymptotic behavior of dissipative systems
    • Amer. Math. Soc., Providence, RI
    • J.K. Hale, Asymptotic behavior of dissipative systems, Math. Surveys and Mon., 25, Amer. Math. Soc., Providence, RI, 1988.
    • (1988) Math. Surveys and Mon. , vol.25
    • Hale, J.K.1
  • 18
    • 0001530660 scopus 로고
    • Attractors of non-autonomous dynamical systems and their dimension
    • V.V. Chepyzhov and M.I. Vishik, Attractors of non-autonomous dynamical systems and their dimension, J. Math. Pures Appl., (3) 73 (1994), 279-333.
    • (1994) J. Math. Pures Appl. , vol.73 , Issue.3 , pp. 279-333
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 20
    • 0031521307 scopus 로고    scopus 로고
    • Evolution equations and their trajectory attractors
    • V.V. Chepyzhov and M.I. Vishik, Evolution equations and their trajectory attractors, J. Math. Pures Appl., (10) 76 (1997), 913-964.
    • (1997) J. Math. Pures Appl. , vol.76 , Issue.10 , pp. 913-964
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 21
    • 0141736942 scopus 로고    scopus 로고
    • Trajectory and global attractors of three-dimensional Navier-Stokes systems
    • M.I. Vishik and V.V. Chepyzhov, Trajectory and global attractors of three-dimensional Navier-Stokes systems, Math. Notes, 71 (2002), 177-193.
    • (2002) Math. Notes , vol.71 , pp. 177-193
    • Vishik, M.I.1    Chepyzhov, V.V.2
  • 22
    • 0000160580 scopus 로고
    • Attractors for damped nonlinear hyperbolic equations
    • J.M. Ghidaglia and R. Temam, Attractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl., 66 (1987), 273-319.
    • (1987) J. Math. Pures Appl. , vol.66 , pp. 273-319
    • Ghidaglia, J.M.1    Temam, R.2
  • 23
    • 0041541910 scopus 로고    scopus 로고
    • Uniform attractors for a strongly damped wave equation with linear memory
    • S. Borini and V. Pata, Uniform attractors for a strongly damped wave equation with linear memory, Asymptotic Anal., (3-4) 20 (1999), 263-277.
    • (1999) Asymptotic Anal. , vol.20 , Issue.3-4 , pp. 263-277
    • Borini, S.1    Pata, V.2
  • 24
    • 33745465400 scopus 로고    scopus 로고
    • 3 with linear memory
    • 3 with linear memory. Math. Meth. Appl. Sci., (7) 23 (2000), 633-653.
    • (2000) Math. Meth. Appl. Sci. , vol.23 , Issue.7 , pp. 633-653
    • Pata, V.1
  • 25
    • 0008379128 scopus 로고    scopus 로고
    • Global attractors for a semilinear hyperbolic equation in viscoelasticity
    • C. Giorgi, J.E. Muñoz Rivera and V. Pata, Global attractors for a semilinear hyperbolic equation in viscoelasticity, J. Math. Anal. Appl., (1) 260 (2001), 83-99.
    • (2001) J. Math. Anal. Appl. , vol.260 , Issue.1 , pp. 83-99
    • Giorgi, C.1    Muñoz Rivera, J.E.2    Pata, V.3
  • 26
    • 0141783096 scopus 로고    scopus 로고
    • Attractors for a damped hyperbolic equation with linear memory
    • V. Pata and A. Zucchi, Attractors for a damped hyperbolic equation with linear memory, Adv. Math. Sci. Appl., (2) 11 (2001), 505-529.
    • (2001) Adv. Math. Sci. Appl. , vol.11 , Issue.2 , pp. 505-529
    • Pata, V.1    Zucchi, A.2
  • 27
    • 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
  • 31
    • 0003306279 scopus 로고
    • Navier-Stokes equations. Theory and numerical analysis
    • North-Holland, Amsterdam, New York, Oxford
    • R. Temam, Navier-Stokes equations. Theory and numerical analysis, Studies in Mathematics and its Applications, 2, North-Holland, Amsterdam, New York, Oxford, 1977.
    • (1977) Studies in Mathematics and Its Applications , vol.2
    • Temam, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.