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Volumn 13, Issue 3, 2005, Pages 553-560

On Fourier parametrization of global attractors for equations in one space dimension

Author keywords

Burgers equation; Determining modes; Global attractor; Inertial manifold

Indexed keywords


EID: 23844488578     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.13.553     Document Type: Article
Times cited : (2)

References (24)
  • 3
    • 0031068506 scopus 로고    scopus 로고
    • Dirichlet quotients for periodic 2 dimensional Navier-Stokes equations
    • P. Constantin, C. Foias, I. Kukavica, and A. Majda, Dirichlet quotients for periodic 2 dimensional Navier-Stokes equations, J. Math Pures Appl. 76 (1997), 125-153.
    • (1997) J. Math Pures Appl. , vol.76 , pp. 125-153
    • Constantin, P.1    Foias, C.2    Kukavica, I.3    Majda, A.4
  • 4
    • 0003088833 scopus 로고
    • Spectral barriers and inertial manifolds for dissipative partial differential equations
    • P. Constantin, C. Foias, B. Nicolaenko, and R. Temam, Spectral barriers and inertial manifolds for dissipative partial differential equations, J. Dynam. Diff. Eq. 1 (1988), 45-73.
    • (1988) J. Dynam. Diff. Eq. , vol.1 , pp. 45-73
    • Constantin, P.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 6
    • 0001047390 scopus 로고
    • Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension
    • C. Foias, B. Nicolaenko, G.R. Sell, and R. Temam, Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension, J. Math. Pures Appl. 67 (1988), 197-226.
    • (1988) J. Math. Pures Appl. , vol.67 , pp. 197-226
    • Foias, C.1    Nicolaenko, B.2    Sell, G.R.3    Temam, R.4
  • 7
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolutionary equations
    • C. Foias, G. R. Sell, and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Diff. Eq. 73 (1988), 309-353.
    • (1988) J. Diff. Eq. , vol.73 , pp. 309-353
    • Foias, C.1    Sell, G.R.2    Temam, R.3
  • 8
    • 0001686992 scopus 로고
    • Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
    • C. Foias, G. R. Sell, and E. S. Titi, Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations, J. Dynam. Diff. Eq. 1 (1989), 199-244.
    • (1989) J. Dynam. Diff. Eq. , vol.1 , pp. 199-244
    • Foias, C.1    Sell, G.R.2    Titi, E.S.3
  • 9
    • 0342670035 scopus 로고
    • Some backward uniqueness results
    • J.-M. Ghidaglia, Some backward uniqueness results, Nonlinear Anal. 10 (1986), 777-790.
    • (1986) Nonlinear Anal. , vol.10 , pp. 777-790
    • Ghidaglia, J.-M.1
  • 10
    • 84990666077 scopus 로고
    • Stability of the Kuramoto-Sivashinsky and related systems
    • J. Goodman, Stability of the Kuramoto-Sivashinsky and related systems, Comm. Pure Appl. Math. 47 (1994), 293-306.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 293-306
    • Goodman, J.1
  • 12
    • 0003293929 scopus 로고
    • Asymptotic behaviour of dissipative systems
    • American Mathematics Society, Providence, R.I.
    • J. K. Hale, Asymptotic behaviour of dissipative systems, Mathematics Surveys and Monographs Vol. 25 (American Mathematics Society, Providence, R.I., 1988).
    • (1988) Mathematics Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 13
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer-Vergal, Berlin
    • D. Henry, "Geometric Theory of Semilinear Parabolic Equations, " Springer Lecture Notes in Mathematics Vol. 840, Springer-Vergal, Berlin, 1984.
    • (1984) Springer Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 14
    • 0003003497 scopus 로고    scopus 로고
    • On the dissipative scale for the Navier-Stokes equation
    • I. Kukavica, On the dissipative scale for the Navier-Stokes equation, Indiana Univ. Math. J. 48 (1999), 1057-1081.
    • (1999) Indiana Univ. Math. J. , vol.48 , pp. 1057-1081
    • Kukavica, I.1
  • 15
    • 23844494894 scopus 로고    scopus 로고
    • Fourier parametrization of attractors for dissipative equations in one space dimension
    • I. Kukavica, Fourier parametrization of attractors for dissipative equations in one space dimension, J. Dynam. Diff. Eq. 15 (2003), 473-484.
    • (2003) J. Dynam. Diff. Eq. , vol.15 , pp. 473-484
    • Kukavica, I.1
  • 16
    • 85039383433 scopus 로고    scopus 로고
    • Backward behavior of solutions of the Kuramoto-Sivashinsky equation
    • to appear
    • I. Kukavica and M. Malcok, Backward behavior of solutions of the Kuramoto-Sivashinsky equation, J. Math. Anal. Appl. (to appear).
    • J. Math. Anal. Appl.
    • Kukavica, I.1    Malcok, M.2
  • 17
    • 0001372244 scopus 로고
    • A sharp condition for existence of an inertial manifold
    • M. Miklavčič, A sharp condition for existence of an inertial manifold, J. Dynam. Differential Equations 3 (1991), 437-456.
    • (1991) J. Dynam. Differential Equations , vol.3 , pp. 437-456
    • Miklavčič, M.1
  • 18
    • 0007341958 scopus 로고
    • Finite-dimensional attracting manifolds in reaction-diffusion equations
    • Nonlinear partial differential equations (Durham, N.H.), Amer. Math. Soc., Providence, R.I.
    • X. Mora, Finite-dimensional attracting manifolds in reaction-diffusion equations, Nonlinear partial differential equations (Durham, N.H., 1982), 353-360, Contemp. Math., 17, Amer. Math. Soc., Providence, R.I., 1983.
    • (1982) Contemp. Math. , vol.17 , pp. 353-360
    • Mora, X.1
  • 19
    • 84968508885 scopus 로고
    • Inertial manifolds for reaction diffusion equations in higher space dimensions
    • J. Mallet-Paret and G.R. Sell, Inertial manifolds for reaction diffusion equations in higher space dimensions, J. Amer. Math. Soc. 1 (1988), 805-866.
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 805-866
    • Mallet-Paret, J.1    Sell, G.R.2
  • 20
    • 0041024672 scopus 로고
    • Lower bounds for solutions of differential inequalities in Hilbert space
    • H. Ogawa, Lower bounds for solutions of differential inequalities in Hilbert space, Proc. Amer. Math. Soc. 16 (1965), 1241-1243.
    • (1965) Proc. Amer. Math. Soc. , vol.16 , pp. 1241-1243
    • Ogawa, H.1
  • 21
    • 0000002115 scopus 로고
    • A concise proof of the "geometric" construction of inertial manifolds
    • J.C. Robinson, A concise proof of the "geometric" construction of inertial manifolds, Phys. Lett. A 200 (1995), 415-417.
    • (1995) Phys. Lett. A , vol.200 , pp. 415-417
    • Robinson, J.C.1
  • 22
    • 0033466968 scopus 로고    scopus 로고
    • Inertial manifolds with and without delay
    • J.C. Robinson, Inertial manifolds with and without delay, Discrete Contin. Dynam. Systems 5 (1999), 813-824.
    • (1999) Discrete Contin. Dynam. Systems , vol.5 , pp. 813-824
    • Robinson, J.C.1
  • 24
    • 0003278399 scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • Springer Publ., New York
    • R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Appl. Math. Sciences No. 68, Springer Publ., New York, 1988.
    • (1988) Appl. Math. Sciences No. 68 , vol.68
    • Temam, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.