Displaying similar documents to “Attractors for general operators”

On the definition of strange nonchaotic attractor

Lluís Alsedà, Sara Costa (2009)

Fundamenta Mathematicae

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The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove...

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.

Remarks on the Fractal Dimension of Bi-Space Global and Exponential Attractors

Jan W. Cholewa, Radoslaw Czaja, Gianluca Mola (2008)

Bollettino dell'Unione Matematica Italiana

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Bi-space global and exponential attractors for the time continuous dynamical systems are considered and the bounds on their fractal dimension are discussed in the context of the smoothing properties of the system between appropriately chosen function spaces. The case when the system exhibits merely some partial smoothing properties is also considered and applications to the sample problems are given.

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.

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...

Irregular attractors.

Anishchenko, Vadim S., Strelkova, Galina I. (1998)

Discrete Dynamics in Nature and Society

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Some models of Cahn-Hilliard equations in nonisotropic media

Alain Miranville (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We derive in this article some models of Cahn-Hilliard equations in nonisotropic media. These models, based on constitutive equations introduced by Gurtin in [19], take the work of internal microforces and also the deformations of the material into account. We then study the existence and uniqueness of solutions and obtain the existence of finite dimensional attractors.

Compact Global Chaotic Attractors of Discrete Control Systems

David Cheban (2014)

Nonautonomous Dynamical Systems

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The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fν(n)(xn), where ν : ℤ+ ⃗ {1,2,...,m}. If m ≥ 2 we give sufficient conditions (the family M := {f1,f2,...,fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework...

Attractors of Strongly Dissipative Systems

A. G. Ramm (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see,...

Global attractor for the perturbed viscous Cahn-Hilliard equation

Maria B. Kania (2007)

Colloquium Mathematicae

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We consider the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation in space dimension n ≤ 3. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space (H²(Ω)∩ H¹₀(Ω)) × L²(Ω) and characterize its structure.