Determining nodes for extended dissipative systems

Nonlinearity

Volumn 9, Issue 5, 1996, Pages 1089-1097

  Collet, Pierre ^a   Titi, Edriss S ^b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040628385     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/9/5/002     Document Type: Article

References (12)

1. Collet P 1994 Thermodynamic limit of the Ginzburg-Landau equation Nonlinearity 7 1175-90
2. Collet P 1994 Non linear parabolic evolutions in unbounded domains Dynamics, Bifurcations and Symmetries ed P Chossat Nato ASI 437 (New York: Plenum) pp 97-104
3. Collet P and Eckmann J-P 1990 The time dependent amplitude equation for the Swift-Hohenberg problem Commun. Math. Phys. 132 139
4. Dupont T and Scott R 1980 Polynomial approximation of functions in Sobolev spaces Math. Comp. 34 441-63
5. Foias C and Kukavica I 1995 Determining nodes for the Kuramoto-Sivashinsy equation J. Dyn. Diff. Eq. to appear
6. Foias C and Temam R 1984 Determination of the solutions of the Navire-Stokes equations by a set of nodal values Math. Comp. 43 117-33
7. Foias C and Titi E S 1991 Determining nodes, finite difference schemes and inertial manifolds Nonlinearity 4 135-53
8. Jones D A and Titi E S 1992 Determination of the solutions of the Navier-Stokes equations by finite volume elements Physica D 60 165-74
9. Jones D A and Titi E S 1993 Upper bounds on the number of determining modes, nodes and volume elements for the Navier-Stokes equations Ind. Univ. Math. J. 42 875-87
10. Kukavica I 1992 On the number of determining nodes for the Ginzburg-Landau equation Nonlinearity 5 997-1006
11. Nehari Z 1975 Conformal Mappings (New York: Dover)
12. Takáč P, Bollerman P, Doelman A, van Harten A and Titi E S 1996 Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation SIAM J. Math. Anal. 27 424-48