76
Views
26
CrossRef citations to date
0
Altmetric
Original Articles

Construction of stochastic inertial manifolds using backward integration

&
Pages 305-324 | Published online: 04 Apr 2007

References

  • Arnold , L. and Scheutzow , M. 1995 . Perfect cocycles through stochastic differential equations . Prob. Theory and Rel. Fields , 101 : 65 – 88 .
  • Bensoussan , A. and Flandoli , F. 1994 . “ Stochastic inertial manifolds, Scuola Normale Superiore di Pisa ” . Preprint No 7
  • Bernal , A. R. 1990 . Inertial manifolds for dissipative semiflows in Banach spaces . Applicable Analysis , 37 : 95 – 141 .
  • Chow , S. N. and Lu , K. 1988 . Invariant manifolds for flows in Banach spaces . J. Differential Equations , 74 : 285 – 317 .
  • Chueshow , I. D. and Girya , T. V. 1994 . Inertial manifolds for stochastic dissipative dynamical systems . Doklady of Acad. Sci. Ukraine , 74 ( 7 ) : 42 – 45 .
  • Constantin , P. , Foias , C. , Nicolaenko , B. and Temam , R. 1988 . “ Integral and inertial manifolds for dissipative partial differential equations ” . New York : Springer Verlag .
  • Crauel , H. , Debussche , A. and Flandoli , F. “ Random attractors ” . Preprint de
  • Da Prato , G. and Zabczyk , J. 1992 . “ Stochastic equations in infinite dimensions ” . In Encyclopedia of Mathematics and its Applications , Cambridge University Press .
  • Debussche , A. 1990 . Inertial manifolds and Sacker's equation . Differential and Integral Equations , 3 : 467 – 486 .
  • Debussche , A. and Temam , R. 1993 . “ Inertial manifolds and their dimensions ” . In Dynamical systems theory and applications 21 – 46 .
  • Fabes , E. , Luskin , M. and Sell , G. R. 1991 . Construction of inertial manifolds by elliptic regularization . J. Differential Equations , 89 : 355 – 387 .
  • Foias , C. , Sell , G. R. and Temam , R. 1988 . Inertial Manifolds For NonLinear Evolutionnary Equations . J. Differential Equations , 73 : 309 – 353 .
  • Mallet-Paret , J. and Sell , G. R. 1988 . Inertial manifolds for reaction-diffusion equation in higher space dimension . J. Amer. Math. Soc. , 1 : 805 – 866 .
  • Pardoux , E. and Peng , S. 1990 . “ Adapted solution of Backward Stochastic Equations ” . In Systems Control Letters Vol. 14 , 55 – 61 .
  • Peng , S. 1993 . Backward Stochastic Differential equations and Applications to Optimal Control . Appl Math. Optim. , 27 : 125 – 144 .
  • Richards , J. 1982 . On the gaps between numbers which are the sum of two squares . Adv. Math. , 46 : 1 – 2 .
  • Sell , G. R. and You . 1991 . “ Inertial manifolds: the non-selfadjoint case ” . Preprint
  • Wanner , T. 1995 . “ Linearization of random dynamical systems ” . In Dynamics Reported , Vol. 4 , Springer Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.