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Title: A permutation characterization of Sturm attractors of Hamiltonian type
Authors: Fiedler, BernoldRocha, CarlosWolfrum, Matthias
Issue Date: 2010
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1573, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We consider Neumann boundary value problems of the form u_t = u_xx + f on the interval leq x leq pi$ for dissipative nonlinearities f = f (u). A permutation characterization for the global attractors of the semiflows generated by these equations is well known, even in the general case f = f (x, u, u_x ). We present a permutation characterization for the global attractors in the restrictive class of nonlinearities f = f (u) this class the stationary solutions of the parabolic equation satisfy the second order ODE v^primeprime + f (v) = 0 and we obtain the permutation characterization from a characterization of the set of 2pi-periodic orbits of this planar Hamiltonian system. Our results are based on a diligent discussion of this mere pendulum equation.
Keywords: Global attractor; Sturm permutation
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
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Appears in Collections:Mathematik



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