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Volumn 12, Issue 1, 2005, Pages 17-39

Integral manifolds and attractors with exponential rate for nonautonomous hyperbolic equations with dissipation

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EID: 15844430128     PISSN: 10619208     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (23)

References (42)
  • 1
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolutionary equations
    • Foias, C., Sell, G. R., and Temam, R., Inertial Manifolds for Nonlinear Evolutionary Equations, J. Diff. Eq., 1988, vol. 73, no. 2, pp. 309-353.
    • (1988) J. Diff. Eq. , vol.73 , Issue.2 , pp. 309-353
    • Foias, C.1    Sell, G.R.2    Temam, R.3
  • 2
    • 0001686992 scopus 로고
    • Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
    • Foias, C., Sell, G. R., and Titi, E. S., Exponential Tracking and Approximation of Inertial Manifolds for Dissipative Nonlinear Equations, J. Dyn. and Diff. Eq., 1989, vol. 1, pp. 199-244.
    • (1989) J. Dyn. and Diff. Eq. , vol.1 , pp. 199-244
    • Foias, C.1    Sell, G.R.2    Titi, E.S.3
  • 4
    • 0007341958 scopus 로고
    • Finite dimensional attracting manifolds in reaction diffusion equations
    • Mora, X., Finite Dimensional Attracting Manifolds in Reaction Diffusion Equations, Contemp. Math., 1983, vol. 17, pp. 353-360.
    • (1983) Contemp. Math. , vol.17 , pp. 353-360
    • Mora, X.1
  • 5
    • 84968508885 scopus 로고
    • Inertial manifolds for reaction-diffusion equations in higher space dimensions
    • Mallet-Paret, J. and Sell, G. R., Inertial Manifolds for Reaction-Diffusion Equations in Higher Space Dimensions, J. Amer. Math. Soc., 1988, vol. 4, no. 4, pp. 805-866.
    • (1988) J. Amer. Math. Soc. , vol.4 , Issue.4 , pp. 805-866
    • Mallet-Paret, J.1    Sell, G.R.2
  • 6
    • 0001372244 scopus 로고
    • A sharp condition for existence of an inertial manifold
    • Miklavčič, M., A Sharp Condition for Existence of an Inertial Manifold, J. Dyn. and Diff. Eq., 1991, vol. 3, no. 3, pp. 437-456.
    • (1991) J. Dyn. and Diff. Eq. , vol.3 , Issue.3 , pp. 437-456
    • Miklavčič, M.1
  • 8
    • 0001830780 scopus 로고
    • Sharp estimates for the dimension of inertial manifolds for nonlinear parabolic equations
    • Romanov, A.V., Sharp Estimates for the Dimension of Inertial Manifolds for Nonlinear Parabolic Equations, Izv. Ross. Akad. Nauk Ser. Mat., 1993, vol. 57, no. 4, pp. 36-54.
    • (1993) Izv. Ross. Akad. Nauk Ser. Mat. , vol.57 , Issue.4 , pp. 36-54
    • Romanov, A.V.1
  • 9
    • 0031319995 scopus 로고    scopus 로고
    • Global integral manifolds with exponential tracking for nonautonomous equations
    • Chepyzhov, V. V. and Goritsky, A. Yu., Global Integral Manifolds with Exponential Tracking for Nonautonomous Equations, Russ. Jour. Math. Phys., 1997, vol. 5, no. 1, pp. 9-28.
    • (1997) Russ. Jour. Math. Phys. , vol.5 , Issue.1 , pp. 9-28
    • Chepyzhov, V.V.1    Goritsky, A.Yu.2
  • 10
    • 15844424484 scopus 로고    scopus 로고
    • Explicit construction of integral manifolds with exponential tracking
    • Chepyzhov, V. V. and Goritsky, A. Yu., Explicit Construction of Integral Manifolds with Exponential Tracking, Appl. Anal., 1999, vol. 71, nos. 1-4, pp. 237-252.
    • (1999) Appl. Anal. , vol.71 , Issue.1-4 , pp. 237-252
    • Chepyzhov, V.V.1    Goritsky, A.Yu.2
  • 11
    • 0009903233 scopus 로고
    • Finite-dimensional attracting invariant manifolds for damped semilinear wave equations
    • Mora, X., Finite-Dimensional Attracting Invariant Manifolds for Damped Semilinear Wave Equations, Res. Notes in Math., 1987, vol. 155, pp. 172-183.
    • (1987) Res. Notes in Math. , vol.155 , pp. 172-183
    • Mora, X.1
  • 12
    • 0002844740 scopus 로고
    • Existence and nonexistence of finite-dimensional globally attracting invariant manifolds in semilinear damped wave equations
    • New York: Springer
    • Mora, X. and Solá-Morales, J., Existence and Nonexistence of Finite-Dimensional Globally Attracting Invariant Manifolds in Semilinear Damped Wave Equations, in: Dynamics of Infinite Dimensional Systems, New York: Springer, 1987, pp. 187-210.
    • (1987) Dynamics of Infinite Dimensional Systems , pp. 187-210
    • Mora, X.1    Solá-Morales, J.2
  • 13
    • 15844363032 scopus 로고    scopus 로고
    • Dichotomy property for solutions of semilinear equations in the problems on inertial manifolds
    • to appear
    • Chepyzhov, V. V. and Goritsky, A. Yu., Dichotomy Property for Solutions of Semilinear Equations in the Problems on Inertial Manifolds, Mat. Sbornik, to appear.
    • Mat. Sbornik
    • Chepyzhov, V.V.1    Goritsky, A.Yu.2
  • 14
    • 15744363098 scopus 로고    scopus 로고
    • Local integral manifolds of a nonautonomous parabolic equation
    • Goritskii [Goritsky], A. Yu. and Vishik, M. I., Local Integral Manifolds of a Nonautonomous Parabolic Equation, Tr. Semin, im. I. G. Petrovskogo, 1997, vol. 19, pp. 304-322; English translation: J. Math. Sci. (New York), 1997, vol. 85, no. 6, pp. 2428-2439.
    • (1997) Tr. Semin, im. I. G. Petrovskogo , vol.19 , pp. 304-322
    • Goritsky, A.Yu.1    Vishik, M.I.2
  • 15
    • 15844378739 scopus 로고    scopus 로고
    • Goritskii [Goritsky], A. Yu. and Vishik, M. I., Local Integral Manifolds of a Nonautonomous Parabolic Equation, Tr. Semin, im. I. G. Petrovskogo, 1997, vol. 19, pp. 304-322; English translation: J. Math. Sci. (New York), 1997, vol. 85, no. 6, pp. 2428-2439.
    • (1997) J. Math. Sci. (New York) , vol.85 , Issue.6 , pp. 2428-2439
  • 17
    • 0346448448 scopus 로고    scopus 로고
    • Global attractor and its perturbations for a dissipative hyperbolic equation
    • Chepyzhov, V. V. and Vishik, M. I., Global Attractor and Its Perturbations for a Dissipative Hyperbolic Equation, Russ. Jour. Math. Phys, 2001, vol. 8, no. 3, pp. 311-330.
    • (2001) Russ. Jour. Math. Phys , vol.8 , Issue.3 , pp. 311-330
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 18
    • 84892997825 scopus 로고
    • Averaging in infinite dimensions
    • Hale, J. K. and Verduyn Lunel, S. M., Averaging in Infinite Dimensions, J. Int. Eq. and Appl., 1990, vol. 2, no. 4, pp. 463-494.
    • (1990) J. Int. Eq. and Appl. , vol.2 , Issue.4 , pp. 463-494
    • Hale, J.K.1    Verduyn Lunel, S.M.2
  • 19
    • 0007147878 scopus 로고    scopus 로고
    • Averaging of dissipative dynamical systems with rapidly oscillating right-hand sides
    • Il'in [Ilyin], A.A., Averaging of Dissipative Dynamical Systems with Rapidly Oscillating Right-Hand Sides, Mat. Sb., 1996, vol. 187, no. 5, pp. 15-58; English translation: Sb. Math., 1996, vol. 187, no. 5, pp. 635-677.
    • (1996) Mat. Sb. , vol.187 , Issue.5 , pp. 15-58
    • Il'in, A.A.1
  • 20
    • 0030505336 scopus 로고    scopus 로고
    • Il'in [Ilyin], A.A., Averaging of Dissipative Dynamical Systems with Rapidly Oscillating Right-Hand Sides, Mat. Sb., 1996, vol. 187, no. 5, pp. 15-58; English translation: Sb. Math., 1996, vol. 187, no. 5, pp. 635-677.
    • (1996) Sb. Math. , vol.187 , Issue.5 , pp. 635-677
  • 23
    • 0348130941 scopus 로고    scopus 로고
    • Averaging of trajectory attractors of evolution equations with rapidly oscillating terms
    • Chepyzhov, V. V. and Vishik, M. I., Averaging of Trajectory Attractors of Evolution Equations with Rapidly Oscillating Terms, Mat. Sb., 2001, vol. 192, no. 1, pp. 13-50; English translation: Sb. Math., 2001, vol. 192, no. 1-2, pp. 11-47.
    • (2001) Mat. Sb. , vol.192 , Issue.1 , pp. 13-50
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 24
    • 15844371158 scopus 로고    scopus 로고
    • Chepyzhov, V. V. and Vishik, M. I., Averaging of Trajectory Attractors of Evolution Equations with Rapidly Oscillating Terms, Mat. Sb., 2001, vol. 192, no. 1, pp. 13-50; English translation: Sb. Math., 2001, vol. 192, no. 1-2, pp. 11-47.
    • (2001) Sb. Math. , vol.192 , Issue.1-2 , pp. 11-47
  • 25
    • 15844389466 scopus 로고    scopus 로고
    • Approximation of trajectories lying on a global attractor of a hyperbolic equation with an exterior force that oscillates rapidly over time
    • Chepyzhov, V. V. and Vishik, M. I., Approximation of Trajectories Lying on a Global Attractor of a Hyperbolic Equation with an Exterior Force That Oscillates Rapidly over Time, Mat. Sb., 2003, vol. 194, no. 9, pp. 3-30; English translation: Sb. Math., 2003, vol. 194, no. 9-10, pp. 1273-1300.
    • (2003) Mat. Sb. , vol.194 , Issue.9 , pp. 3-30
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 26
    • 0742323510 scopus 로고    scopus 로고
    • Chepyzhov, V. V. and Vishik, M. I., Approximation of Trajectories Lying on a Global Attractor of a Hyperbolic Equation with an Exterior Force That Oscillates Rapidly over Time, Mat. Sb., 2003, vol. 194, no. 9, pp. 3-30; English translation: Sb. Math., 2003, vol. 194, no. 9-10, pp. 1273-1300.
    • (2003) Sb. Math. , vol.194 , Issue.9-10 , pp. 1273-1300
  • 27
    • 0742315524 scopus 로고    scopus 로고
    • Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating terms
    • Fiedler, B. and Vishik, M.I., Quantitative Homogenization of Global Attractors for Hyperbolic Wave Equations with Rapidly Oscillating Terms, Uspekhi Mat. Nauk, 2002, vol. 57, no. 4, pp. 75-94; English translation: Russian Math. Surveys, 2002, vol. 57, no. 4, pp. 709-728.
    • (2002) Uspekhi Mat. Nauk , vol.57 , Issue.4 , pp. 75-94
    • Fiedler, B.1    Vishik, M.I.2
  • 28
    • 0036664157 scopus 로고    scopus 로고
    • Fiedler, B. and Vishik, M.I., Quantitative Homogenization of Global Attractors for Hyperbolic Wave Equations with Rapidly Oscillating Terms, Uspekhi Mat. Nauk, 2002, vol. 57, no. 4, pp. 75-94; English translation: Russian Math. Surveys, 2002, vol. 57, no. 4, pp. 709-728.
    • (2002) Russian Math. Surveys , vol.57 , Issue.4 , pp. 709-728
  • 29
    • 15744391353 scopus 로고    scopus 로고
    • Non-autonomous 2D Navier-Stokes system with a simple global attractor and some averaging problems
    • Chepyzhov, V. V. and Vishik, M.I., Non-Autonomous 2D Navier-Stokes System with a Simple Global Attractor and Some Averaging Problems, El. J. ESAIM: COCV, 2002, vol. 8, pp. 467-487.
    • (2002) El. J. ESAIM: COCV , vol.8 , pp. 467-487
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 30
    • 84894031064 scopus 로고    scopus 로고
    • Quantitative homogenization of analytic semigroups and reaction-diffusion equations with diophantine spatial sequences
    • Fiedler, B. and Vishik, M.I., Quantitative Homogenization of Analytic Semigroups and Reaction-Diffusion Equations with Diophantine Spatial Sequences, Advances in Diff. Eg., 2001, vol. 6, no. 11, pp. 1377-1408.
    • (2001) Advances in Diff. Eg. , vol.6 , Issue.11 , pp. 1377-1408
    • Fiedler, B.1    Vishik, M.I.2
  • 31
    • 0346724398 scopus 로고    scopus 로고
    • Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization
    • Efendiev, M. and Zelik, S., Attractors of the Reaction-Diffusion Systems with Rapidly Oscillating Coefficients and Their Homogenization, Ann. I.H. Poincaré, 2002, vol. 19, no. 6, pp. 961-989.
    • (2002) Ann. I.H. Poincaré , vol.19 , Issue.6 , pp. 961-989
    • Efendiev, M.1    Zelik, S.2
  • 32
    • 2642513860 scopus 로고    scopus 로고
    • The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging
    • Efendiev, M. and Zelik, S., The Regular Attractor for the Reaction-Diffusion System with a Nonlinearity Rapidly Oscillating in Time and Its Averaging, Advances in Diff. Eq., 2003, vol. 8, pp. 673-732.
    • (2003) Advances in Diff. Eq. , vol.8 , pp. 673-732
    • Efendiev, M.1    Zelik, S.2
  • 33
    • 15744402000 scopus 로고    scopus 로고
    • On non-autonomous Sine-Gordon type equations with a simple global attractor and some averaging
    • Chepyzhov, V. V., Vishik, M.I., and Wendland, W. L., On Non-Autonomous Sine-Gordon Type Equations with a Simple Global Attractor and Some Averaging, Discr. and Cont. Dyn. Syst., 2005, vol. 12, no. 1, pp. 27-38.
    • (2005) Discr. and Cont. Dyn. Syst. , vol.12 , Issue.1 , pp. 27-38
    • Chepyzhov, V.V.1    Vishik, M.I.2    Wendland, W.L.3
  • 39
    • 0000633043 scopus 로고
    • A Hausdorff dimension estimate for kernel sections of non-autonomous evolution equations
    • Chepyzhov, V.V. and Vishik, M.I., A Hausdorff Dimension Estimate for Kernel Sections of Non-Autonomous Evolution Equations, Indiana Univ. Math. J., 1993, vol. 42, no. 3, pp. 1057-1076.
    • (1993) Indiana Univ. Math. J. , vol.42 , Issue.3 , pp. 1057-1076
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 42
    • 0010457587 scopus 로고    scopus 로고
    • Unbounded one-dimensional global attractor for the damped Sine-Gordon equation
    • Qian, M., Qin, W.-X., Wang, G.-X., and Zhu, S., Unbounded One-Dimensional Global Attractor for the Damped Sine-Gordon Equation, J. Nonlinear Sci., 2000, vol. 10, no. 4, pp. 417-432.
    • (2000) J. Nonlinear Sci. , vol.10 , Issue.4 , pp. 417-432
    • Qian, M.1    Qin, W.-X.2    Wang, G.-X.3    Zhu, S.4


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