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The Exponential Attractors for the g-Navier-Stokes Equations [PDF]
Journal of Function Spaces and Applications, 2012 We consider the exponential attractors for the two-dimensional g-Navier-Stokes equations in bounded domain Ω. We establish the existence of the exponential attractor in L2(Ω).
Delin Wu, Jicheng Tao
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GLOBAL AND EXPONENTIAL ATTRACTORS FOR THE PENROSE–FIFE SYSTEM [PDF]
Mathematical Models and Methods in Applied Sciences, 2009 The Penrose–Fife system for phase transitions is addressed. Dirichlet boundary conditions for the temperature are assumed. Existence of global and exponential attractors is proved. Differently from preceding contributions, here the energy balance equation is both singular at 0 and degenerate at ∞.
Schimperna, Giulio
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Strong Exponential Attractors for Weakly Damped Semilinear Wave Equations [PDF]
Journal of Mathematics, 2020 In this paper, we investigate the longtime dynamics for the damped wave equation in a bounded smooth domain of ℝ3. The exponential attractor is investigated in a strong energy space for the case of subquintic nonlinearity, which is based on the recent ...
Cuncai Liu, Fengjuan Meng, Chang Zhang
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Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions [PDF]
Journal of Applied Mathematics, 2013 We study exponential attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains. First, we give the existence of the exponential attractor in by proving that the corresponding semigroup satisfies the enhanced ...
Zhao-hui Fan
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Open sets of Axiom A flows with exponentially mixing attractors [PDF]
Proceedings of the American Mathematical Society, 2016 For any dimension d ≥ 3 d\geq 3 we construct C 1 \mathcal {C}^{1} -open subsets of the space of C 3 \mathcal {C}^{3} vector fields such that the flow associated to each vector ...
Ara('u)jo, V. +2 more
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Electronic Journal of Differential Equations, 2018 Under consideration is the damped semilinear wave equation $$ u_{tt}+u_t-\Delta u+u+f(u)=0 $$ in a bounded domain $\Omega$ in $\mathbb{R}^3$ subject to an acoustic boundary condition with a singular perturbation, which we term "massless acoustic ...
Joseph L. Shomberg
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Exponential attractors for a nonclassical diffusion equation
Electronic Journal of Differential Equations, 2009 In this article, we prove the existence of exponential attractors for a nonclassical diffusion equation in ${H^{2}(Omega)}cap{H}^{1}_{0}(Omega)$ when the space dimension is less than 4.
Qiaozhen Ma, Yong-Feng Liu
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Chevron Pattern Equations: Exponential Attractor and Global Stabilization [PDF]
Vietnam Journal of Mathematics, 2021 The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state solution through application of a finite-dimensional feedback control is proved in two spatial dimensions.
Habiba Kalantarova +2 more
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Quasi-stability and continuity of attractors for nonlinear system of wave equations
Nonautonomous Dynamical Systems, 2021 In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces.
Freitas M. M. +4 more
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Existence of exponential attractors for the coupled system of suspension bridge equations
Boundary Value Problems, 2023 In this paper, we investigate the asymptotic behavior of the coupled system of suspension bridge equations. Under suitable assumptions, we obtain the existence of exponential attractors by using the decomposing technique of operator semigroup.
Jun-dong Jin
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