May  2008, 9(3&4, May): 555-580. doi: 10.3934/dcdsb.2008.9.555

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

1. 

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States

2. 

Department of Mathematics, Indiana University, Bloomington, IN, 47405, United States

3. 

Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Ilha do Fundão, Rio de Janeiro, RJ 21941-909, Brazil

4. 

Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States

Received  February 2007 Revised  October 2007 Published  February 2008

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.
Citation: L. Dieci, M. S Jolly, Ricardo Rosa, E. S. Van Vleck. Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 555-580. doi: 10.3934/dcdsb.2008.9.555
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