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On the nonlinear stabilization of the wave equation

100%

Guesmia A.

Annales Polonici Mathematici

1998

tom 68

nr 2

191-198

We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.

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

63%

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

1 Annales Polonici Mathematici

1 Open Mathematics

1 Guesmia A.

1 Pražák D.

1 2003

1 1998

Wyniki wyszukiwania

On the nonlinear stabilization of the wave equation

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