Mathematics – Dynamical Systems
Scientific paper
2009-12-07
Mathematics
Dynamical Systems
16 pages, 5 figures
Scientific paper
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing such manifolds for kinetic models using trajectory optimization. The corresponding objective functional reflects a variational principle that characterizes trajectories on, respectively near, slow invariant manifolds. For a two-dimensional linear system and a common nonlinear test problem we show analytically that the variational approach asymptotically identifies the exact slow invariant manifold in the limit of both an infinite time horizon of the variational problem with fixed spectral gap and infinite spectral gap with a fixed finite time horizon. Numerical results for the linear and nonlinear model problems as well as a more realistic higher-dimensional chemical reaction mechanism are presented.
Lebiedz Dirk
Siehr Jochen
Unger Jonas
No associations
LandOfFree
A variational principle for computing slow invariant manifolds in dissipative dynamical systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A variational principle for computing slow invariant manifolds in dissipative dynamical systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A variational principle for computing slow invariant manifolds in dissipative dynamical systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-243729