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Minimal periods of semilinear evolution equations with Lipschitz nonlinearity
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UNSPECIFIED (2006) Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. JOURNAL OF DIFFERENTIAL EQUATIONS, 220 (2). pp. 396-406. doi:10.1016/j.jde.2005.04.009 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2005.04.009
Abstract
It is known that any periodic orbit of a Lipschitz ordinary differential equation x = f(x) must have period at least 2 pi/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 alpha with 0 <= alpha <= 1/2 there exists a constant K-alpha such that if L is the Lipschitz constant of f as a map from D(A(alpha)) into H then any periodic orbit has period at least KalphaL-1/(1-alpha). 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. (c) 2005 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Journal or Publication Title: | JOURNAL OF DIFFERENTIAL EQUATIONS | ||||
| Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | ||||
| ISSN: | 0022-0396 | ||||
| Official Date: | 15 January 2006 | ||||
| Dates: |
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| Volume: | 220 | ||||
| Number: | 2 | ||||
| Number of Pages: | 11 | ||||
| Page Range: | pp. 396-406 | ||||
| DOI: | 10.1016/j.jde.2005.04.009 | ||||
| Publication Status: | Published |
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