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Dynamics of periodically forced parabolic equations on the circle

  • Björn Sandstede (a1) and Bernold Fiedler (a1)

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.

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Dynamics of periodically forced parabolic equations on the circle

  • Björn Sandstede (a1) and Bernold Fiedler (a1)

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