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  1. 3 Open Mathematics

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  1. 3 Pražák D.

  2. 1 Žabenský J.

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  1. 1 2013

  2. 1 2006

  3. 1 2003

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On the dynamics of equations with infinite delay

100%
Pražák D.
Open Mathematics
|
2006
|
tom 4
|
nr 4
635-647
EN
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.
2
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A necessary and sufficient condition for the existence of an exponential attractor

100%
Pražák D.
Open Mathematics
|
2003
|
tom 1
|
nr 3
411-417
EN
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.
3
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On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model

63%
Pražák D., Žabenský J.
Open Mathematics
|
2013
|
tom 11
|
nr 7
1264-1282
EN
We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ɛΔ3. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ɛ > 0.
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