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Applicable Analysis
An International Journal
Volume 70, 1998 - Issue 3-4
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Original Articles

Intertial sets for a model of convection in a porous medium and for its time discretization

Time discretization

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Pages 363-384 | Received 01 Feb 1998, Published online: 20 Jan 2011

References

  • Babin , A. V. and Vishik , M. I. 1992 . Attractors of evolution equations , Amsterdam : North Holland .
  • Bories , S. and Combarnous , M. 1975 . Hydrothermal convection in saturated porous media . Adv. Hydrosci , 10 : 231 – 307 .
  • Eden , A. , Foias , C. , Nicolaenko , B. and Temam , R. 1994 . Exponential attractors for dissipative evolution equations , Vol. 37 , Masson john Wiley publ .
  • Fabrie , P. 1986 . Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieu poreux . Acta Applicandae Mathematicae , 7 : 49 – 77 .
  • Fabrie , P. 1989 . Solutions fortes et majorations asymptotiques pour le modèle de Darcy—Forchheimer en convection naturelle . Annales Faculté des Sciences de Toulouse , X : 7 – 26 .
  • Fabrie , P. and Nicolaenko , B. 1995 . Exponential attractors for non dissipative systems modeling convection in porous media , Mathématiques Appliquées de Bordeaux . Rapport Interne 95012
  • Fujiwara , D. and Morimoto , H. 1977 . An Lp—theorem of the Helmholtz decomposition of vector fields . J. Fac. Sci. Univ Tokyo A1 , 24 : 685 – 700 .
  • Hale , J. K. 1988 . “ Asymptotic behavior of dissipative systems ” . In Math. Surveys and Monographs , Vol. 25 , AMS .
  • Hale , J. K. , Lin , X. B. and Raugel , G. 1988 . Upper-semicontinuity of attractors for approzimations of semigroups and partial differential equations . Math. of Computation , 5 : 89 – 123 .
  • Kapitanskii , L. V. and Kostin , I. N. 1990 . Attractors of nonlinear evolution equations and their approximations . Algebra i Analiz 2:l , 40 : 97 – 117 . English translation: Leningrad Math. J. 2:l (1991)
  • Ladyzhenskya , O. A. 1982 . On finite dimesionality of bounded invariant sets for the Navier-Stokes equatons and some other dissipative systems . Zap. Nauchn. Semin LOMI , 115 ( 1 ) : 137 – 155 .
  • Ladyzhenskaya , O. A. 1991 . Attractors for semigroups and evolution equations , Cambridge : Cambridge University Press .
  • Solonnikov , V. A. 1973 . Estimates of solutions of evolution Navier-Stokes system . Zap. Nauchn. Semin. LOMI , 38 : 153 – 231 .
  • Temam , R. 1988 . “ Infinite-dimensional dynamical systems in mechanics and physics ” . In Appl. Math. Sci , Vol. 68 , Springer-Verlag .

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