Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation

L. Dieci; M. S Jolly; Ricardo Rosa; E. S. Van Vleck

doi:10.3934/dcdsb.2008.9.555

Article Contents

2008, Volume 9, Issue 3&4: 555-580. Doi: 10.3934/dcdsb.2008.9.555

This issue Previous Article On the spectrum of the one-dimensional Schrödinger operator Next Article Equi-Attraction and the continuous dependence of attractors on time delays

Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation

1.
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
2.
Department of Mathematics, Indiana University, Bloomington, IN, 47405
3.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Ilha do Fundão, Rio de Janeiro, RJ 21941-909
4.
Department of Mathematics, University of Kansas, Lawrence, KS 66045

Received: January 31, 2007

Revised: September 30, 2007

Published: April 2008

Abstract Related Papers Cited by

Abstract

We provide an analysis of the error in approximating Lyapunov exponents of dissipative PDEs on inertial manifolds using QR techniques. The reduction in the number of modes needed for an inertial form facilitates the error analysis. Numerical computations on the Kuramoto-Sivashinsky equation illustrate the results.

Keywords:

Lyapunov exponents,
inertial manifolds.

Mathematics Subject Classification: 35F20, 35Q35, 58F39, 65L, 65M70.

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Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation

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