Abstract
Let be \(\bar \sum \) the inertial manifold constructed in Chapter 10. We recall that £ is smooth and that \(\bar \sum \) is parametrized by B n = {u|P n u = u, |u| ≤ R} through the Lipschitz function \(\Phi :{\bar B_n} \to \bar \sum \) of the Lipschitz constant 4/3. Thus, as long as p = P n p, |p| < R,Φ (p)∈£, it follows that∂Φ(p)/∂pί, ί = 1,…, n, satisfy |∂Φ(p)/∂Φp i | ≤ 4/3. Let B denote the ball in H, B = {u| |u| < R}.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Constantin, P., Foias, C., Nicolaenko, B., Teman, R. (1989). Lower Bound for the Exponential Rate of Convergence to the Attractor. In: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Applied Mathematical Sciences, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3506-4_12
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3506-4_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8131-3
Online ISBN: 978-1-4612-3506-4
eBook Packages: Springer Book Archive