Results 321 to 330 of about 5,198,351 (376)

Global Attractor of One Nonlinear Parabolic Equation

Ukrainian Mathematical Journal, 2003
Let \(\Omega \) be a domain in \(\mathbb R^n\) with smooth boundary \(\partial \Omega \), \(\Omega_T:=[0,T]\times \Omega \). The authors consider the Cauchy-Dirichlet problem \[ \begin{gathered} u_t=a\Delta u-f(u)+\lambda u+\langle {\mathbf b}({\mathbf x}),\nabla u \rangle -g({\mathbf x});\tag{1} \\ u\big|_{\partial \Omega}=0,\quad u\big|_{t=0}=u_0 ...
Kapustyan, O. V., Shkundin, D. V.
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Cycles and Global Attractors of Reaction Systems

2014
Reaction systems are a recent formal model inspired by the chemical reactions that happen inside cells and possess many different dynamical behaviours. In this work we continue a recent investigation of the complexity of detecting some interesting dynamical behaviours in reaction system. We prove that detecting global behaviours such as the presence of
Formenti, E, MANZONI, LUCA, PORRECA, ANTONIO ENRICO   +2 more
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Nonstandard analysis of global attractors

Mathematical Logic Quarterly, 2015
Key concepts of the theory of abstract dynamical systems are formulated in the language of nonstandard analysis (NSA). We are then able to provide simple and intuitive proofs of the basic facts. In particular, we use the NSA to give an alternative proof of the characterization of global attractors due to Ball. We also address the issue of connectedness.
Pražák, Dalibor, Slavík, Jakub
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Global attractor for Hirota equation

Applied Mathematics-A Journal of Chinese Universities, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Ruifeng, Guo, Boling
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Global attractors for a vegetation model

Asymptotic Analysis, 2011
In this article, a rigorous mathematical treatment of the dryland vegetation model introduced by Gilad et al. [Phys. Rev. Lett. 98(9) (2004), 098105-1–098105-4, J. Theoret. Biol. 244 (2007), 680–691] is presented. We prove the existence and uniqueness of solutions in (L1(Ω))3 and the existence of global attractors in L1(Ω;𝒟), where 𝒟 is an invariant ...
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Consequences Regarding the Global Attractor

1989
Let X be the global attractor of the dissipative system under consideration. Recall that X is the largest set in H with the properties (i) S(t)X = X for t ≥ 0, (ii) X is bounded in H, (iii) dist(S(t)uo,X) → 0 as t → ∞ for all uo ∈ H.
P. Constantin, C. Foias, B. Nicolaenko, R. Teman   +3 more
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Global Attractors and a Lubrication Problem

2016
We start this chapter from necessary background on the theory of fractal dimension. Next, we formulate and study a problem which models the two-dimensional boundary driven shear flow in lubrication theory. After the derivation of the energy dissipation rate estimate and a version of Lieb–Thirring inequality we provide an estimate from above on the ...
Grzegorz Łukaszewicz, Piotr Kalita
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Global attractors in competitive systems

Nonlinear Analysis: Theory, Methods & Applications, 1991
This paper deals with the 2-dimensional discrete dynamical system \[ x_ i'=x_ i\lambda_ i(x_ 1+x_ 2),\quad i=1,2, \] on \({\mathbb{R}}^ 2_+=[0,\infty)\times [0,\infty)\). The per capita growth rates \(\lambda_ i\) are assumed to be continuous maps from \({\mathbb{R}}^ 1_+\) to \({\mathbb{R}}^ 1_+\). The resulting map \(F:\;{\mathbb{R}}^ 2_+\to {\mathbb{
Franke, John E., Yakubu, Abdul-Aziz
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Global attractors for autonomous evolution equations

2012
Chapter 2 is concerned with large time behaviour of solutions of evolution equations in terms of the global attractor, its existence and properties. Note that, good estimates on the dimension of attractors in terms of biological (medical, physical etc.) parameters are crucial for the finite-dimensional reduction and at present there exists a highly ...
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Global attractors and approximate inertial

Applicable Analysis, 1993
An abstract nonautonomous differential equation, u' + Au + F(u) = f ( t ) , is considered using assumptions appropriate for systems of reaction-diffusion equations on multi-dimensional spatial domains. A priori estimates establish the existence of absorbing balls in relevant function spaces, and nonsequently the existence of a global attractor is ...
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