Time-averaging under fast periodic forcing of parabolic partial differential equations: Exponential estimates

Journal of Differential Equations

Volumn 174, Issue 1, 2001, Pages 133-180

  Matthies, Karsten ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035920037     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3934     Document Type: Article

References (17)

1. Abraham R., Robbin J. Transversal Mappings and Flows. 1967;Benjamin, New York.
2. Adams R. Soblev Spaces. 1975;Academic Press, New York.
3. Alouges F., Debusssche A. On the qualitative behaviour of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point. Numer. Funct. Anal. Optimiz. 12:1991;253-269.
4. Bates P., Lu K. A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equation. J. Dynam. Differential Equations. 6:1994;101-145.
5. Cao C., Rammaha M., Titi E. Gevrey regularity for nonlinear analytic parabolic equations on the sphere. J. Dynam. Differential Equations. 12:2000;411-433.
6. Ferrari A., Titi E. Gevrey regularity for nonlinear analytic parabolic equations. Comm. Partial Differential Equations. 23:1998;1-16.
7. Fiedler B. Global Hopf bifurcation of two-parameter flows. Arch. Rat. Mech. Anal. 94:1986;59-81.
8. Fiedler B., Scheurle J. Discretization of Homoclinic Orbits, Rapid Forcing and Invisible Chaos. Memoirs AMS. 570:1996;Amer. Math. Soc. Providence.
9. Foias C., Temam R. Gevrey class regularity for the solution of the Navier-Stokes equations. J. Funct. Anal. 87:1989;359-369.
10. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics. 840:1983;Springer-Verlag, New York.
11. Ilyin A. Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides. Sb. Math. 187:1998;635-677.
12. Lu K. A Hartman-Grobman theorem for scalar reaction-diffusion equations. J. Differential Equations. 93:1991;364-394.
13. Neishtadt A. On the separation of motions in systems with rapidly rotating phase. J. Appl. Math. Mech. 48:1984;134-139.
14. Promislow K. Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differential equations. Nonlinear Anal. 16:1991;959-980.
15. Stuart A. Perturbation theory for infinite dimensional dynamical systems. Ainsworth M., Levesley J., Light W. A., Merletta M. Theory and Numerics of Ordinary and Partial Differential Equations. Advances in Numerical Analysis. IV:1995;181-290 Clarendon Press, Oxford.
16. Temam R. Navier-Stokes Equations. Studies in Mathematics and Its Applications. 2:1977;North-Holland, Amsterdam.
17. Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Applied Mathematical Sciences. 68:1988;Springer-Verlag, New York.