Dynamics of trajectories and the finite-dimensional reduction of dissipative evolution equations

Abstract

We consider a general class of evolution equations with nonlinear dissipation. Under minimal regularity assumptions, we show that the large-time dynamics can be uniquely described by a system of ODEs with infinite, but exponentially decaying memory.

The existence of a finite-dimensional attractor is another corollary.

Keywords

• Dynamics
• trajectories
• finite-dimensional
• reduction
• dissipative
• evolution
• equations