Explicit construction of integral manifolds with exponential tracking

Abstract

A nonautonomous evolution equation in a Hilbert space is considered. A simple explicit construction of a finite-dimensional integral manifold with exponential tracking is proposed under the optimal spectral gap assumption. The dependence of the integral manifold on the initial surface is studied. Applications to one and two-dimensional nonautonomous reaction-diffusion systems are considered.

Keywords:

• Inertial and integral manifolds
• exponential tracking

AMS:

• 35B40
• 35K55
• 35K57