Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators [PDF]
, 2011 We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we prove their existence for this model, supporting the fact that the long-term
G. Giacomin +2 more
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Global attractors for a class of degenerate diffusion equations
Electronic Journal of Differential Equations, 2003 In this paper we give two existence results for a class of degenerate diffusion equations with p-Laplacian. One is on a unique global strong solution, and the other is on a global attractor.
Shingo Takeuchi, Tomomi Yokota
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Dynamics of a damped quintic wave equation with time-dependent coefficients
AIMS MathematicsWe present a comprehensive investigation of the long-term dynamics generated by a semilinear wave equation with time-dependent coefficients and quintic nonlinearity on a bounded domain subject to Dirichlet boundary conditions.
Feng Zhou +3 more
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Global attractors for p-Laplacian equation
Journal of Mathematical Analysis and Applications, 2007 AbstractThe existence of a (L2(Ω),W01,p(Ω)∩Lq(Ω))-global attractor is proved for the p-Laplacian equation ut−div(|∇u|p−2∇u)+f(u)=g on a bounded domain Ω⊂Rn (n⩾3) with Dirichlet boundary condition, where p⩾2. The nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c1|u|q−k⩽f(u)u⩽c2|u|q+k and f′(u)⩾−l, where q⩾2 is ...
Chengkui Zhong, Meihua Yang, Chunyou Sun
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Global attractor and finite dimensionality for a class of dissipative equations of BBM's type
Electronic Journal of Differential Equations, 1998 In this work we study the Cauchy problem for a class of nonlinear dissipative equations of Benjamin-Bona-Mahony's type. We discuss the existence of a global attractor and estimate its Hausdorff and fractal dimensions.
M.A. Astaburuaga +3 more
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Asymptotic behavior for second order lattice dynamical systems
Discrete Dynamics in Nature and Society, 2001 We consider the existence of the global attractor for a second order lattice dynamical systems.
Shengfan Zhou
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Global attractor for a nonlinear viscoelastic model
Journal of Mathematical Analysis and Applications, 2008 AbstractIn this paper we establish the existence of global attractors of a semiflow and a semigroup for a nonlinear 1-d viscoelasticity in two frameworks. We exploit the properties of the analytic semigroup to show the compactness for the semiflow and semigroup generated by the weak global solutions.
Yuming Qin, Tzon-Tzer Lu
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The Existence of a Global Attractor for the S-K-T Competition Model with Self-Diffusion
Abstract and Applied Analysis, 2014 This paper concerns the uniform bounds of the global existence of solutions in time for the S-K-T competition model with self-diffusion.
Qian Xu, Ye Zhao
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Global attractors for the extensible thermoelastic beam system
Journal of Differential Equations, 2009 This work is focused on the dissipative system describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of the temperature. Under natural boundary conditions, we prove the existence of bounded absorbing sets.
GIORGI, Claudio +3 more
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Viral Infection Model with Diffusion and Distributed Delay: Finite-Dimensional Global Attractor. [PDF]
Qual Theory Dyn Syst, 2023 Rezounenko A.
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