IJPAM: Volume 40, No. 1 (2007)

DYNAMICS OF TRAJECTORIES
AND THE FINITE-DIMENSIONAL REDUCTION
OF DISSIPATIVE EVOLUTION EQUATIONS

Dalibor Prazák
Department of Mathematical Analysis
Faculty of Mathematics and Physics
Charles University
Sokolovská 83, Prague 8, 186 75, CZECH REPUBLIC
e-mail: prazak@karlin.mff.cuni.cz


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.

Received: August 2, 2007

AMS Subject Classification: 35K90, 35B41, 37L25

Key Words and Phrases: abstract parabolic equation, dynamics of trajectories, finite-dimensional attractor, reduction to ODEs with delay

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 1