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Minimal periods of semilinear evolution equations with Lipschitz nonlinearity

Robinson, James C. and Vidal López, Alejandro (2006) Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. Journal of Differential Equations, 220 (2). pp. 396-406. ISSN 0022-0396

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Abstract

It is known that any periodic orbit of a Lipschitz ordinary differential equation must have period at least 2π/L, where L is the Lipschitz constant of f. In this paper, we prove a similar result for the semilinear evolution equation du/dt=-Au+f(u): for each α with 0 α 1/2 there exists a constant Kα such that if L is the Lipschitz constant of f as a map from D(Aα) into H then any periodic orbit has period at least KαL-1/(1-α). As a concrete application we recover a result of Kukavica giving a lower bound on the period for the 2d Navier–Stokes equations with periodic boundary conditions.


Item Type:Article
Uncontrolled Keywords:Period orbits; Minimal period; Semilinear evolution equations; Navier–Stokes equations
Subjects:Sciences > Mathematics > Differential equations
ID Code:12584
Deposited On:13 Apr 2011 08:37
Last Modified:06 Feb 2014 09:27

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