Displaying similar documents to “Remarks on the Fractal Dimension of Bi-Space Global and Exponential Attractors”

On the dynamics of equations with infinite delay

Dalibor Pražák (2006)

Open Mathematics

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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.

Global attractors for a tropical climate model

Pigong Han, Keke Lei, Chenggang Liu, Xuewen Wang (2023)

Applications of Mathematics

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This paper is devoted to the global attractors of the tropical climate model. We first establish the global well-posedness of the system. Then by studying the existence of bounded absorbing sets, the global attractor is constructed. The estimates of the Hausdorff dimension and of the fractal dimension of the global attractor are obtained in the end.

Attractors for general operators

Alain Miranville (2003)

Applications of Mathematics

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In this article we introduce the notion of a minimal attractor for families of operators that do not necessarily form semigroups. We then obtain some results on the existence of the minimal attractor. We also consider the nonautonomous case. As an application, we obtain the existence of the minimal attractor for models of Cahn-Hilliard equations in deformable elastic continua.

On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization

Ahmad Makki (2016)

Applications of Mathematics

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We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term called the nonlinear Willmore regularization. First, we are interested in the well-posedness of these two models. Furthermore, we prove that both models possess a global attractor. In addition, as far as the viscous Allen-Cahn equation is concerned, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. Finally, we give...

Global Attractor for the Convective Cahn-Hilliard Equation

Xiaopeng Zhao, Changchun Liu (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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This paper is concerned with the convective Cahn-Hilliard equation. We use a classical theorem on existence of a global attractor to derive that the convective Cahn-Hilliard equation possesses a global attractor on some subset of H².