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The principle of spatial averaging and inertial manifolds for reaction-diffusion equations

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Nonlinear Semigroups, Partial Differential Equations and Attractors

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References

  1. E. Conway, D. Hoff, J. Smoller, (1978) large time behavior of solutions of nonlinear reaction-diffusion equations. SIAM J. Appl. Math., 35, #11, p. 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Constantin, C. Foias, B. Nicolaenko, R. Temam, (1986) Integral manifolds and intertial manifolds for dissipative partial differential equations. To appear.

    Google Scholar 

  3. C. Foias, B. Nicolaenko, G.R. Sell, R. Temam, (1985) Variétés inertielles pour l'équation de Kuramoto-Sivashkinsky, C.R. Acad. Sc. Paris, Serie 1, 301, p. 285–288.

    MathSciNet  MATH  Google Scholar 

  4. C. Foias, B. Nicolaenko, G.R. Sell, R. Temam, (1986) Inertial manifold for the Kuramoto Sivashinsky equation. To appear.

    Google Scholar 

  5. C. Foias, G.R. Sell, R. Temam, (1985) Variétés Inertielles des équations differentielles dissipatives, C.R. Acad. Sci. Paris, Serie 1, 301, p. 139–141.

    MathSciNet  MATH  Google Scholar 

  6. C. Foias, G.R. Sell, R. Temam (1986) Inertial manifolds for nonlinear evolutionary equations, IMA Preprint No. 234.

    Google Scholar 

  7. J.K. Hale, L.T. Magalhaes, W.M. Oliva, (1984) An Introduction to Infinite Dimensional Dynamical Systems-Geometric Theory. Appl. Math. Sciences No. 47, Springer-Verlag, Berlin-Heidelberg-New York.

    Book  MATH  Google Scholar 

  8. G.H. Hardy, E.M. Wright, (1962) An Introduction to the Theory of Numbers. Oxford Press.

    Google Scholar 

  9. D. Henry, (1981) Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, No. 840, Springer-Verlag, Berlin-Heidelberg-New York.

    MATH  Google Scholar 

  10. M. Hirsch, C. Pugh, M. Shub, (1977) Invariant Manifolds. Lecture Notes in Mathematics, No. 583, Springer-Verlag, Berlin-Heidelberg-New York.

    MATH  Google Scholar 

  11. J. Mallet-Paret, (1976) Negatively invariant sets of compact maps and an extension of a Theorem of Cartwright, J. Diff. Eqns., 22, p. 331–348.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Mallet-Paret, G.R. Sell (1986a) Inertial manifolds for reaction-diffusion equations in higher space dimension. To appear.

    Google Scholar 

  13. J. Mallet-Paret, G.R. Sell (1986b) A counterexample to the existence of inertial manifolds. To appear.

    Google Scholar 

  14. J. Richards, (1982) On the gaps between numbers which are the sum of two squares, Adv. Math., vol. 46, pp. 1–2.

    Article  MathSciNet  MATH  Google Scholar 

  15. R.J. Sacker, G.R. Sell, (1980) The spectrum of an invariant submanifold, J. Diff. Eqns., vol. 38, p. 135–160.

    Article  MathSciNet  MATH  Google Scholar 

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Tepper L. Gill Woodford W. Zachary

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© 1987 Springer-Verlag

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Mallet-Paret, J., Sell, G.R. (1987). The principle of spatial averaging and inertial manifolds for reaction-diffusion equations. In: Gill, T.L., Zachary, W.W. (eds) Nonlinear Semigroups, Partial Differential Equations and Attractors. Lecture Notes in Mathematics, vol 1248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077419

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  • DOI: https://doi.org/10.1007/BFb0077419

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  • Print ISBN: 978-3-540-17741-8

  • Online ISBN: 978-3-540-47791-4

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