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Dynamics of periodically forced parabolic equations on the circle

Published online by Cambridge University Press:  19 September 2008

Björn Sandstede  and
Bernold Fiedler
Björn Sandstede
Affiliation:
Mathematics Institute A, University of Stuttgart, Pfoffenwaldring 57, 7000 Stuttgart 80, Germany
Bernold Fiedler
Affiliation:
Mathematics Institute A, University of Stuttgart, Pfoffenwaldring 57, 7000 Stuttgart 80, Germany
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Abstract

We consider the dynamics of scalar reaction-diffusion equations:

We show that every prescribed vectorfield in the plane embeds into equation (1) for a suitable f = f (t, x, u, ux). In contrast, suppose f = f (t, u, ux) is independent of x and T-periodic in t. Then the ω-limit set of any bounded solution is a subset of some two-dimensional torus carrying a linear flow.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 3 , September 1992 , pp. 559 - 571
Copyright
Copyright © Cambridge University Press 1992

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References

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