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On the dynamics of equations with infinite delay

100%

Pražák D.

Open Mathematics

2006

tom 4

nr 4

635-647

We consider a system of ordinary differential equations with infinite delay. We study large time dynamics in the phase space of functions with an exponentially decaying weight. The existence of an exponential attractor is proved under the abstract assumption that the right-hand side is Lipschitz continuous. The dimension of the attractor is explicitly estimated.

Finite dimensional global attractor for a class of doubly nonlinear parabolic equations

100%

Miranville A.

Open Mathematics

2006

tom 4

nr 1

163-182

Our aim in this paper is to study the long time behavior of a class of doubly nonlinear parabolic equations. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.

A necessary and sufficient condition for the existence of an exponential attractor

84%

Pražák D.

Open Mathematics

2003

tom 1

nr 3

411-417

We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.

Ograniczanie wyników

3 Open Mathematics

2 Pražák D.

1 Miranville A.

2 2006

1 2003

Wyniki wyszukiwania

On the dynamics of equations with infinite delay

Finite dimensional global attractor for a class of doubly nonlinear parabolic equations

A necessary and sufficient condition for the existence of an exponential attractor