Inertial manifolds of damped semilinear wave equations

Xavier Mora; Joan Solà-Morales

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1989)

  • Volume: 23, Issue: 3, page 489-505
  • ISSN: 0764-583X

How to cite

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Mora, Xavier, and Solà-Morales, Joan. "Inertial manifolds of damped semilinear wave equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 23.3 (1989): 489-505. <http://eudml.org/doc/193574>.

@article{Mora1989,
author = {Mora, Xavier, Solà-Morales, Joan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {global attractor; qualitative dynamics; semilinear damped wave equation},
language = {eng},
number = {3},
pages = {489-505},
publisher = {Dunod},
title = {Inertial manifolds of damped semilinear wave equations},
url = {http://eudml.org/doc/193574},
volume = {23},
year = {1989},
}

TY - JOUR
AU - Mora, Xavier
AU - Solà-Morales, Joan
TI - Inertial manifolds of damped semilinear wave equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1989
PB - Dunod
VL - 23
IS - 3
SP - 489
EP - 505
LA - eng
KW - global attractor; qualitative dynamics; semilinear damped wave equation
UR - http://eudml.org/doc/193574
ER -

References

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  1. [1] S. ANGENENT, The Morse-Smale property for a semilinear parabolic equation, J. Diff. Eq. 62 (1986), 427-442. Zbl0581.58026MR837763
  2. [2] A. V. BABIN, M. I. VISHIK, Uniform asymptotics of the solutions of singularly perturbed evolution equations (in russian), Uspekhi Mat. Nauk 42(5) (1987),231-232. 
  3. [3] S. N. CHOW, K. LU, Invariant manifolds for flows in Banach spaces, J. Diff. Eq. 74 (1988), 285-317. Zbl0691.58034MR952900
  4. [4] J. K. HALE, L. T. MAGALHÂES, W. M. OLIVA, An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory, Springer (1984). Zbl0533.58001MR725501
  5. [5] J. K. HALE, G. RAUGEL, Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Diff. Eq. 73 (1988), 197-214. Zbl0666.35012MR943939
  6. [6] P. HARTMAN, On local homeomorphisms of Euclidean spaces, Bol. Soc, MatMexicana 5 (1960), 220-241. Zbl0127.30202MR141856
  7. [7] D. B. HENRY, Some infinite-dimensional Morse-Smale Systems defined byparabolic partial differential equations, J. Diff. Eq. 59 (1985), 165-205. Zbl0572.58012MR804887
  8. [8] X. MORA, Finite-dimensional attracting invariant manifolds for damped semilinear wave equations, Res. Notes in Math. 155 (1987), 172-183. Zbl0642.35061MR907731
  9. [9] X. MORA, J. SOLÀ-MORALES, Existence and non-existence of finite-dimensional globally attracting invariant manifolds in semilinear damped wave equations, in « Dynamics of Infinite Dimensional Systems » (edited by S. N. Chow, J. K. Hale), Springer (1987), 187-210. Zbl0642.35062MR921912
  10. [10] X. MORA, J. SOLÀ-MORALES, The singular limit dynamics of semilinear damped wave equations, J. Diff, Eq. 78 (1989), 262-307. Zbl0699.35177MR992148
  11. [11] A. VANDERBAUWHEDE, S. A. VAN GILS, Center manifolds and contractionson a scale of Banach spaces, J. Funct. Anal 72 (1987), 209-224. Zbl0621.47050MR886811

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