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Asymptotic symmetry in strongly monotone skew-product semiflows with applications

Yi Wang

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Recommended by C-Q Cheng

For strongly monotone skew-product semiflows on which a compact connected group acts, it is shown that any stable minimal set is residually symmetric and any uniformly stable trajectory is asymptotically symmetric. These results are then applied to study the spatio-temporal asymptotics of stable solutions of reaction–diffusion equations on a symmetric domain in time-recurrent structures including almost periodicity. In particular, the 1-covering property of omega-limit sets is established for uniformly stable bounded solutions of reaction–diffusion equations on a ball.


PACS

02.30.Jr Partial differential equations

05.60.-k Transport processes

MSC

35K57 Reaction-diffusion equations

35K55 Nonlinear PDE of parabolic type

37C65 Monotone flows

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 4 (April 2009)

Received 11 July 2008, in final form 16 January 2009

Published 26 February 2009



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