@phdthesis{BJHTUP11_1989__0245__P0_0, author = {Debussche, Arnaud}, title = {Quelques probl\`emes concernant le comportement pour les grands temps des \'equations d'\'evolution dissipatives}, series = {Th\`eses d'Orsay}, publisher = {Universit\'e de Paris-Sud Centre d'Orsay}, number = {245}, year = {1989}, language = {fr}, url = {http://www.numdam.org/item/BJHTUP11_1989__0245__P0_0/} }
TY - BOOK AU - Debussche, Arnaud TI - Quelques problèmes concernant le comportement pour les grands temps des équations d'évolution dissipatives T3 - Thèses d'Orsay PY - 1989 IS - 245 PB - Université de Paris-Sud Centre d'Orsay UR - http://www.numdam.org/item/BJHTUP11_1989__0245__P0_0/ LA - fr ID - BJHTUP11_1989__0245__P0_0 ER -
%0 Book %A Debussche, Arnaud %T Quelques problèmes concernant le comportement pour les grands temps des équations d'évolution dissipatives %S Thèses d'Orsay %D 1989 %N 245 %I Université de Paris-Sud Centre d'Orsay %U http://www.numdam.org/item/BJHTUP11_1989__0245__P0_0/ %G fr %F BJHTUP11_1989__0245__P0_0
Debussche, Arnaud. Quelques problèmes concernant le comportement pour les grands temps des équations d'évolution dissipatives. Thèses d'Orsay, no. 245 (1989), 116 p. http://numdam.org/item/BJHTUP11_1989__0245__P0_0/
[1] Asymptotic behaviour of dissipative systems, Mathematical Surveys and Monographs, Vol. 25, AMS, Providence. | MR | Zbl
[2] Infinite dimensional dynamical systems in mechanics and physics, Applied mathematics Series, Vol.68, Springer-Verlag, New-York, 1988 | MR | Zbl
[3] On the nature of turbulence, Comm. math. Phys., 20, 167-192, 1971. | MR | Zbl | DOI
and[4] Differentiable dynamical systems, Bull. Amer. Math. Soc., 73, 747-817, 1967. | MR | Zbl | DOI
[5] Global bifurcation and chaos, Applied mathematics Series, Vol. 73, Springer-Verlag, New-York, 1988. | MR | Zbl
[6] A new approach to the perturbation theory of invariant surfaces, Comm. on Pure and Applied Math., Vol.XVIII, 717-732, 1965. | MR | Zbl | DOI
[7] Approximate inertial manifolds for reaction diffusion equations in high space dimension, Dynamics and Differential Equations, to appear. | MR | Zbl
[8] Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation, Proc. Luminy Workshop on Dynamical Systems, 1987, to appear. | MR | Zbl | Numdam
[9] Some global dynamical properties of a class of pattern formation equation, Comm. Partial Diff. Equ., 14 (2), 245-297, 1989. | MR | Zbl | DOI
, and[10] Upper semi continuity of the attractor for a singularly perturbed hyperbolic equation, J. Diff. Equ., 73, 197-214, 1988. | MR | Zbl | DOI
andInvariant manifolds for flows in Banach spaces, Journal of differential equations 74, 285-317 (1988). | MR | Zbl | DOI
and [1]Nouvaux résultats sur les variétés inertelles pour les équations différentielles dissipatives C.R. Acad. Sci. Paris, Ser. I, 302 375-378 (1986). | MR | Zbl
, , , [1]Integral and Inertial Manifolds for dissipative partial differential equations, Springer-Verlag, New-York, to appear. | Zbl | DOI
, , , [2]Spectral barriers and inertial manifolds for dissipative partial differential equations, to appear. | MR | Zbl | DOI
, , , [3]Methods of mathematical physics, Intersciences publishers, New-York (1953). | MR | Zbl
et [1]Construction of inertial manifolds by elliptic regularization, IMA preprint series # 459, Minneapolis, 1988. | MR | Zbl
, and [1]Variétés inertielles pour l'équation de Kuramoto-Sivashinsky, C.R. Acad. Sci. Paris, Ser. I, 301 285-288 (1985). | MR | Zbl
, , and [1]Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension, IMA preprint series # 279 (1986) | MR | Zbl
, , and [2]Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension, J. Math. Pures Appl., to appear (1988). | MR | Zbl
, , and [2]Sur l'interaction des petits et grands tourbillons dans les écoulements turbulents, C.R. Acad Sci. Paris, Série I, 305 497-500 (1987). | MR | Zbl
, and [1]Modelization of the interaction of small and large eddies in turbulent flows, Math. Mod. and Num. Anal. M2AN (1988). | MR | Zbl | Numdam
, and [2]Variétés inertielles des équations différentielles dissipatives, C.R. Acad. Sci. Paris, Série. I, 301 139-142 (1985). | MR | Zbl
, and [1]Inertial manifols for nonlinear evolutionary equations, J. diff. equations, 73, 1988, p.309-353. | MR | Zbl | DOI
, and [2]Elliptic Partial Diffeerential Equations of Second Order, 2nd Ed., Springer-Verlag, New-York (1983). | MR | Zbl
and [1]Asymptotic Behavior of dissipative systems, Mathematical Surveys and Monographs, Vol. 25, AMS, Providence (1988). | MR | Zbl
[1]Approximation theories for inertial manifolds, M2AN, vol. 23, 1989. | MR | Zbl | Numdam | DOI
and [1]Inertial manifols for reaction diffusion equation in higher space dimension, J. Americ math soc., Volume 1, Number 4, Octobre 1988, p.805-866. | MR | Zbl | DOI
and [1]Approximate inertial manifolds for reaction diffusion equations in high-space dimension, Dynamic and differential equations, to appear. | MR | Zbl
[1]Approximate inertial manifolds for the pattern formation Cahn Hilliard equation, Infinite dimensional dynamical systems, J.C. Saut et R. Temam Eds. | Zbl | Numdam
[2]A new approach to the perturbation theory of invariant surfaces, Comm. on Pure and Applied Math., Vol. XVIII, 717-732 (1965). | MR | Zbl | DOI
[1]Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New-York (1988). | MR | Zbl | DOI
[1]Variété inertielle approchée pour les équations de Navier-Stokes bidimensionnelles, C.R. Acad. Sci. Paris, Ser. II, 306 399-402 (1988). | MR | Zbl
[2][1] Attractors of partial differential equations and estimates of their dimension. Russ. Math. Surv. 38:4, 1983, 151-213. | Zbl | MR
and ,[2] Spinodal decomposition, Trans. Met. Soc. of AIME, 248, 1968, 166-180.
,[3] Free energy of a non uniform system I. Interfacial free energy, J. Chem. Phys. 28, 1958, 258-267. | Zbl | DOI
and ,[4] Spectral barriers and inertial manifolds for dissipative partial differential equations, J. Dynamics and Differential Equations, 1, 1989, 45-73. | MR | Zbl | DOI
, , , ,[5] Inertial manifolds and Sacker's equation, Differential and Integral Equations, to appear. | MR | Zbl
,[6] Construction of inertial manifolds by elliptic regularization, IMA Preprint No. 459, 1988. | MR | Zbl
, and ,[7] Modelling of the interaction of small and large eddies in two dimensional turbulent flows, Math. Modelling Numerical Anal., 22, 1988, 93-118. | MR | Zbl | Numdam
, and ,[8] Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations, 73, 1988, 309-353. | MR | Zbl | DOI
, and ,[9] Approximate inertial manifolds for the Kuramoto-Sivashinsky equation : analysis and computations, Mathematical Sciences Institute Technical Report, Cornell University, 1989, Submitted to Physica D. | MR | Zbl
, , and ,[10] Bounds on complexity in reaction-diffusion systems, SIAM J. Appl. Math., 46, 1986, 68-80. | MR | Zbl | DOI
and ,[11] Theory of spinodal decomposition in alloys, Ann. of Phys., 65, 1971, 53-86. | DOI
,[12] Inertial manifolds for reaction-diffusion equations in higher space dimension, J. Amer. Math. Soc. 1, 1989, 805-866. | MR | Zbl | DOI
and ,[13]
and , (In preparation).[14] Attractors for reaction-diffusion equations : existence and estimate of their dimension, Appl. Anal. , 25, 1987, 101-147. | MR | Zbl | DOI
,[15] Approximate inertial manifolds for reaction-diffusion equations in high space dimension, J. Dynamics and Differential Equations, 1, 1989, 245-267. | MR | Zbl | DOI
,[16] Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation, Math. Modelling Numerical Anal, 23, 1989, 463-480. | MR | Zbl | Numdam
,[17] Nonlinear Galerkin methods, SIAM J. Num. Anal. 26, 1989, 1139-1157. | MR | Zbl | DOI
and ,[18] Existence and non-existence of finite-dimensional globally attracting invariant manifolds in semilinear damped wave equations, Dynamics of Infinite Dimensional Systems, Springer-Verlag, New-York, 187-210. | MR | Zbl
and ,[19] Low-dimensional behavior of the pattern formation Cahn-Hilliard equation, in Trends in the Theory and Practice of Nonlinear Analysis., V. Lakshmikantham ed., North-Holland, 1985. | MR | Zbl
and ,[20] Some global dynamical properties of a class of pattern formation equations, Comm. Partial Diff. Equ., | MR | Zbl
, and ,[21] Nonlinear aspects of the Cahn-Hilliard equation, Physica D, 10, 1984, 277-298. | MR | DOI
and ,[22] Thesis, 1989, Université Paris-sud, Orsay, France.
,[23]
and .[24] Approximation dynamics : hyperbolic sets and inertial manifolds, University of Minnesota Supercolmputer Institute, 1989, Preprint No. 89/39.
,[25] Attractors for the Navier-Stokes equations : localization and approximation, J. of the fac. of Sci. of Tokyo, to appear. | MR | Zbl
,[26] Une variété approximante de I'attracteur universel des équations de Navier-Stokes, non linéaire, de dimension finie, C.R. Acad. Sci. , Série I., Paris, 307, 1988, 383-385. | MR | Zbl
,Attractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl., 66, 1987, 273-310. | MR | Zbl
and [1]Upper semi-continuity of the attractor for a singularly perturbed hyperbolic equation, J. Diff. Equ., 73, 1988, 197-214. | MR | Zbl | DOI
and [1]Lower semi-continuity of the attractor for a singularly perturbed hyperbolic equation, to appear. | MR | Zbl
and [2]Nonhomogeneous boundary value problems and applicatoins, Springer Verlag, New-York, 1972. | Zbl
and [1]Some global dynamical properties of a class of pattern formation equations, Comm. Partial Differential Equ., 14(2), 1989, 245-297. | MR | Zbl | DOI
, and [1]Comportement de dimension finie pour les équations de Schrödinger faiblement amorties. | Zbl
[1]Infinite dimensional dynamical systems in mechanics and physics, Applied Mathematics Series, vol. 68, Springer-Verlag, New-York, 1988. | MR | Zbl
[1]Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs, vol. 25, AMS, Providence, 1988. | MR | Zbl
[1]