메뉴 건너뛰기




Volumn 8, Issue 4, 2002, Pages 815-833

Computing inertial manifolds

Author keywords

Approximate inertial manifolds; Inertial manifolds

Indexed keywords


EID: 0036788830     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2002.8.815     Document Type: Article
Times cited : (21)

References (30)
  • 2
    • 0003368378 scopus 로고
    • Integral manifolds and inertial manifolds for dissipative partial differential equations
    • P. Constantin, C. Foias, B. Nicolaenko and R. Temam, "Integral manifolds and inertial manifolds for dissipative partial differential equations" (Springer AMS 70, 1988).
    • (1988) Springer AMS , vol.70
    • Constantin, P.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 4
    • 44949278926 scopus 로고
    • Inertial manifolds for partial differential evolution equations under time discretization: Existence, convergence, and applications
    • F. Demengel and J.M. Ghidaglia, Inertial manifolds for partial differential evolution equations under time discretization: existence, convergence, and applications, J. Math. Anal. Appl. 155 (1991), 177-225.
    • (1991) J. Math. Anal. Appl. , vol.155 , pp. 177-225
    • Demengel, F.1    Ghidaglia, J.M.2
  • 6
    • 0000076092 scopus 로고
    • Variétés inertielles des équations différentielles dissipatives
    • C. Foias, G.R. Sell and R. Temam, Variétés inertielles des équations différentielles dissipatives, C. R. Acad. Sci. Paris I 301 (1985), 139-141.
    • (1985) C. R. Acad. Sci. Paris I , vol.301 , pp. 139-141
    • Foias, C.1    Sell, G.R.2    Temam, R.3
  • 8
    • 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
  • 9
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolution equations
    • C. Foias, G.R. Sell and R. Temam, Inertial Manifolds for nonlinear evolution 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
  • 10
    • 0000640737 scopus 로고
    • Modelling of the interaction of small and large eddies in two dimensional turbulent flows
    • C. Foias, O. Manley and R. Temam, Modelling of the interaction of small and large eddies in two dimensional turbulent flows, Math. Mod. Num. Anal. 22 (1988), 93-114.
    • (1988) Math. Mod. Num. Anal. , vol.22 , pp. 93-114
    • Foias, C.1    Manley, O.2    Temam, R.3
  • 11
    • 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. Dyn. Diff. Eq. 1 (1989), 199-244.
    • (1989) J. Dyn. Diff. Eq. , vol.1 , pp. 199-244
    • Foias, C.1    Sell, G.R.2    Titi, E.S.3
  • 12
  • 13
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer-Verlag, New York
    • D. Henry, "Geometric Theory of Semilinear Parabolic Equations" (Lecture Notes in Math. Vol 840, Springer-Verlag, New York, 1981).
    • (1981) Lecture Notes in Math. , vol.840
    • Henry, D.1
  • 14
    • 0000868591 scopus 로고
    • Attractive invariant manifolds under approximation - Inertial manifolds
    • D.A. Jones and A.M. Stuart, Attractive invariant manifolds under approximation - inertial manifolds, J. Diff. Eq. 123 (1995), 588-637.
    • (1995) J. Diff. Eq. , vol.123 , pp. 588-637
    • Jones, D.A.1    Stuart, A.M.2
  • 15
    • 0010599996 scopus 로고    scopus 로고
    • Persistence of invariant sets for partial differential equations
    • D.A. Jones, A.M. Stuart and E.S. Titi, Persistence of invariant sets for partial differential equations, J. Math. Anal. Appl. 219 (1998) 479-502.
    • (1998) J. Math. Anal. Appl. , vol.219 , pp. 479-502
    • Jones, D.A.1    Stuart, A.M.2    Titi, E.S.3
  • 16
    • 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
  • 17
    • 84923279813 scopus 로고
    • Extension of range of functions
    • E.J. McShane, Extension of range of functions, Bull. Amer. Math. Soc. 40 (1934), 837-842.
    • (1934) Bull. Amer. Math. Soc. , vol.40 , pp. 837-842
    • McShane, E.J.1
  • 18
    • 84972560880 scopus 로고
    • Stability for semilinear equations with noninvertible linear operator
    • M. Miklavčič, Stability for semilinear equations with noninvertible linear operator, Pacific J. Math. 118 (1985), 199-214.
    • (1985) Pacific J. Math. , vol.118 , pp. 199-214
    • Miklavčič, M.1
  • 19
    • 0001372244 scopus 로고
    • A sharp condition for the existence of an inertial manifold
    • M. Miklavčič, A sharp condition for the existence of an inertial manifold, J. Dyn. Diff. Eq. 3 (1991), 437-456.
    • (1991) J. Dyn. Diff. Eq. , vol.3 , pp. 437-456
    • Miklavčič, M.1
  • 21
    • 0000005730 scopus 로고
    • Inertial manifolds and the cone condition
    • J.C. Robinson, Inertial manifolds and the cone condition, Dyn. Sys. Appl. 2 (1993), 311-330.
    • (1993) Dyn. Sys. Appl. , vol.2 , pp. 311-330
    • Robinson, J.C.1
  • 22
    • 4243533637 scopus 로고
    • Ph.D. Thesis, University of Cambridge
    • J.C. Robinson, "Inertial manifolds" (Ph.D. Thesis, University of Cambridge, 1995).
    • (1995) Inertial manifolds
    • Robinson, J.C.1
  • 23
    • 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
  • 24
    • 0010534874 scopus 로고    scopus 로고
    • Some closure results for inertial manifolds
    • J.C. Robinson, Some closure results for inertial manifolds, J. Dyn. Diff. Eq. 9 (1997) 373-400.
    • (1997) J. Dyn. Diff. Eq. , vol.9 , pp. 373-400
    • Robinson, J.C.1
  • 25
    • 0031534626 scopus 로고    scopus 로고
    • Convergent families of inertial manifolds for convergent approximations
    • J.C. Robinson, Convergent Families of Inertial Manifolds for Convergent Approximations, Numerical Algorithms 14 (1997) 179-188.
    • (1997) Numerical Algorithms , vol.14 , pp. 179-188
    • Robinson, J.C.1
  • 26
    • 0033466968 scopus 로고    scopus 로고
    • Inertial manifolds with and without delay
    • J.C. Robinson, Inertial manifolds with and without delay, Disc. Cont. Dyn. Sys. 5 (1999) 813-824.
    • (1999) Disc. Cont. Dyn. Sys. , vol.5 , pp. 813-824
    • Robinson, J.C.1
  • 28
    • 0001843014 scopus 로고
    • Inertial manifolds for dissipative semiflows in Banach spaces
    • A. Rodriguez Bernal, Inertial manifolds for dissipative semiflows in Banach spaces, Appl. Anal. 37 (1990), 95-141.
    • (1990) Appl. Anal. , vol.37 , pp. 95-141
    • Bernal, A.R.1
  • 29
    • 0009139403 scopus 로고
    • An optimality condition for approximate inertial manifolds
    • G.R. Sell, C. Foias and R. Temam, R. (Eds.), "Turbulence in Fluid Flows: A dynamical systems approach", (Springer, New York)
    • G.R. Sell, An optimality condition for approximate inertial manifolds, in G.R. Sell, C. Foias and R. Temam, R. (Eds.), "Turbulence in Fluid Flows: A dynamical systems approach" (IMA Volumes in Mathematics and its Applications 55, Springer, New York, 1993).
    • (1993) IMA Volumes in Mathematics and its Applications , vol.55
    • Sell, G.R.1
  • 30
    • 0003278399 scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics" (Springer AMS 68, 1988).
    • (1988) Springer AMS , vol.68
    • Temam, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.