Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory

Journal of Function Spaces ◽

10.1155/2017/4896161 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10

Author(s):

Xiaobin Yao ◽

Qiaozhen Ma

Keyword(s):

Global Attractor ◽

Function Method ◽

Global Attractors ◽

Nonlinear Damping ◽

Kirchhoff Type ◽

Contraction Function ◽

Plate Equations

We prove in this paper the existence of a global attractor for the plate equations of Kirchhoff type with nonlinear damping and memory using the contraction function method.

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Existence of global attractors for wave equation of Kirchhoff type with nonlinear damping and memory term at boundary

Dynamics of Partial Differential Equations ◽

10.4310/dpde.2007.v4.n3.a3 ◽

2007 ◽

Vol 4 (3) ◽

pp. 247-262 ◽

Cited By ~ 4

Author(s):

Chaosheng Zhu

Keyword(s):

Wave Equation ◽

Global Attractors ◽

Nonlinear Damping ◽

Memory Term ◽

Kirchhoff Type

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Global attractor for the Kirchhoff type equations with strong nonlinear damping and supercritical nonlinearity

Applied Mathematics Letters ◽

10.1016/j.aml.2014.02.014 ◽

2014 ◽

Vol 33 ◽

pp. 12-17 ◽

Cited By ~ 12

Author(s):

Zhijian Yang ◽

Pengyan Ding ◽

Zhiming Liu

Keyword(s):

Global Attractor ◽

Nonlinear Damping ◽

Kirchhoff Type ◽

Supercritical Nonlinearity

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Kolmogorov‚Äôs √•-Entropy for a Class of Invariant Sets and Dimension of Global Attractors for Second- Order Evolution Equations with Nonlinear Damping

Lecture Notes in Pure and Applied Mathematics - Control Theory of Partial Differential Equations ◽

10.1201/9781420028317.ch4 ◽

2005 ◽

pp. 51-69 ◽

Cited By ~ 4

Author(s):

Irena Lasiecka ◽

Igor Chueshov

Keyword(s):

Evolution Equations ◽

Global Attractors ◽

Nonlinear Damping ◽

Second Order ◽

Invariant Sets

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Global Attractors for the Higher-Order Evolution Equation

Applied Mathematics and Nonlinear Sciences ◽

10.2478/amns.2020.1.00018 ◽

2020 ◽

Vol 5 (1) ◽

pp. 195-210

Author(s):

Erhan Pişkin ◽

Hazal Yüksekkaya

Keyword(s):

Asymptotic Behavior ◽

Evolution Equation ◽

Global Solution ◽

Global Attractor ◽

Type Equation ◽

Global Attractors ◽

Higher Order ◽

Evolution Type

AbstractIn this paper, we obtain the existence of a global attractor for the higher-order evolution type equation. Moreover, we discuss the asymptotic behavior of global solution.

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Global attractor for the Kirchhoff type equation with a strong dissipation

Journal of Differential Equations ◽

10.1016/j.jde.2010.09.024 ◽

2010 ◽

Vol 249 (12) ◽

pp. 3258-3278 ◽

Cited By ~ 16

Author(s):

Yang Zhijian ◽

Wang Yunqing

Keyword(s):

Global Attractor ◽

Type Equation ◽

Kirchhoff Type ◽

Kirchhoff Type Equation

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Exponential global attractors for semigroups in metric spaces with applications to differential equations

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385710000702 ◽

2011 ◽

Vol 31 (6) ◽

pp. 1641-1667 ◽

Cited By ~ 3

Author(s):

ALEXANDRE N. CARVALHO ◽

JAN W. CHOLEWA

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Global Attractor ◽

Metric Space ◽

Metric Spaces ◽

Global Attractors ◽

Invariant Sets ◽

Bounded Subset ◽

Partial Differential ◽

Unstable Manifolds

AbstractIn this article semigroups in a general metric space V, which have pointwise exponentially attracting local unstable manifolds of compact invariant sets, are considered. We show that under a suitable set of assumptions these semigroups possess strong exponential dissipative properties. In particular, there exists a compact global attractor which exponentially attracts each bounded subset of V. Applications of abstract results to ordinary and partial differential equations are given.

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