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Global Attractor of One Nonlinear Parabolic Equation
Ukrainian Mathematical Journal, 2003Let \(\Omega \) 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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Global attractors and bifurcations
1996We present some recent developments in the study of attractors of smooth dynamical systems, specially attractors whose basin has a global character. A key point in our approach is to explore the relations between this study and that of main bifurcation mechanisms.
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On the Theory of Global Attractors and Lyapunov Functionals
Set-Valued and Variational Analysis, 2012This work is devoted to the study of the existence of global attractors for multivalued and single-valued semigroups, more specifically, under which conditions a multivalued (or single-valued) semigroup \(\{S(t): t\geqslant 0\}\) possesses a global attractor \(\mathcal{A}\).
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Consequences Regarding the Global Attractor
1989Let 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 +3 more
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Global Attractors and a Lubrication Problem
2016We 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 for autonomous evolution equations
2012Chapter 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, 1993An 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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Global attractors for piezoelectric solids
ANNALI DELL UNIVERSITA DI FERRARA, 2004The Galerkin method is applied to study an hyperbolic-elliptic initial-boundary value problem in the theory of piezoelectric solids. We prove that the semigroup generated by the corresponding dynamical system has a global attractor.
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Global Attractors of Nonautonomous Difference Equations
2006The article is devoted to the study of global attractors of quasi-linear non-autonomous difference equations, in particular we give the conditions for the existence of a compact global attractor. The obtained results are applied to the study of a triangular economic growth model recently developed by Brianzoni S., Mammana C. and Michetti E.
D. CHEBAN +2 more
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Attractor-repeller approach for global placement
1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051), 2003Hussein Etawil +2 more
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