Skip to main content
Log in

Attractors of periodic processes and estimates of their dimension

  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A. V. Babin and M. I. Vishik, Attractors for Evolutionary Equations [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  2. J. K. Hale, “Asymptotic behavior of dissipative systems,” Mathematical Surveys and Monographs,25, Amer. Math. Soc., Providence (1987).

    Google Scholar 

  3. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, 1988.

  4. J. M. Ghidaghlia and R. Temam, “Attractors for damped nonlinear hyperbolic equations,” J. Math. Pures Appl.,66, 273–319 (1987).

    MathSciNet  Google Scholar 

  5. A. Haraux, “Attractors of asymptotically compact processes and applications to nonlinear partial differential equations,” Preprint: Univer. Pierre et Marie Curie, Centre National de la Recherce Scientifique, No. 87031 (1987).

  6. A. Haraux, Systèmes Dinamiques Dissipatifs et Applications, Masson, Paris-Milan-Barcelona-Rome (1991).

    Google Scholar 

  7. V. V. Chepyzhov and M. I. Vishik, “Attractors of nonautonomous dynamical systems and their dimension,” J. Math. Pures Appl.,73, No. 3, 279–333 (1994).

    MathSciNet  Google Scholar 

  8. V. V. Chepyzhov and M. I. Vishik, “Nonautonomous dynamical systems and their attractors,” Appendix to Aymptotic Behavior of Solutions of Evolutionary Equations by M. I. Vishik, Cambridge University Press (1992).

  9. V. V. Chepyzov and M. I. Vishik, “Nonautonomous evolution equations and their attractors,” Russ. J. Math. Physics,1, No. 2, 165–190 (1993).

    Google Scholar 

  10. V. V. Chepyzov and M. I. Vishik, “A Hausdorff dimension estimates for kernel sections of nonautonomous evolution equations,” Indiana Univ. Math. J.,42, No. 3, 1057–1076 (1993).

    MathSciNet  Google Scholar 

  11. O. F. Ladyzhenskaya, Mathematical Problems in the Dynamics of Viscous Incompressible Fluids [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  12. R. Temam, On the Theory and Numerical Analysis of the Navier-Stokes Equations, Springer-Verlag (1974).

  13. A. V. Babin and M. I. Vishik, “Attractors for evolutionary partial differential equations and bounds for their dimensions,” UMN,38, No. 4, 133–187 (1983).

    MathSciNet  Google Scholar 

  14. V. V. Chepyzov and M. I. Vishik, “Periodic processes and nonautonomous evolution equations with time-periodic terms,” in: Volume in Honour of J. Leary (1994).

  15. J.-L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires, Dunod, Paris (1969).

    Google Scholar 

  16. C. M. Dafermos, “Almost periodic processes and almost periodic solutions of evolutional equations,” in: Proc. Univ. Florida International Symposium, Academic Press, New York (1977), pp. 43–57.

    Google Scholar 

  17. LaSalle, “Stability theory and invariance principles,” in: Dynamical Systems, Vol. 1, Academic Press, New York (1976), pp. 211–222.

    Google Scholar 

  18. G. R. Sell, “Nonautonomous differential equations and topological dynamics, I, II,” Am. Math. Soc.,127, 241–262, 263–283 (1967).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was partially supported by grants from the Russian Fund for Basic Research and grant No. MR5000 from the International Scientific Fund.

Translated from Matematicheskie Zametki, Vol. 57, No. 2, pp. 181–202, February, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vishik, M.I., Chepyzhov, V.V. Attractors of periodic processes and estimates of their dimension. Math Notes 57, 127–140 (1995). https://doi.org/10.1007/BF02309145

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02309145

Keywords

Navigation