Results 71 to 80 of about 1,961 (190)
Electronic Journal of Differential Equations, 2016 In this article, we prove the existence of pullback attractor in $C([-h,0];H^1(\mathbb{R}^N))$ for a stochastic nonclassical diffusion equations on unbounded domains with non-autonomous deterministic and stochastic forcing terms, and the pullback ...
Fang-Hong Zhang, Wei Han
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Criteria for strong and weak random attractors
, 2008 The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak ...
B. Schmalfuß +19 more
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Random Attractors of Stochastic Three-Component Reversible Gray-Scott System on Unbounded Domains
Abstract and Applied Analysis, 2012 The existence of a pullback random attractor is established for a stochastic three-component reversible Gray-Scott system on unbounded domains. The Gray-Scott system is recast as a random dynamical system and asymptotic compactness which is illustrated ...
Anhui Gu
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The Pullback Attractors for the Nonautonomous Camassa‐Holm Equations [PDF]
Mathematical Problems in Engineering, 2009 We consider the pullback attractors for the three‐dimensional nonautonomous Camassa‐Holm equations in the periodic box Ω = [0, L] 3. Assuming , which is translation bounded, the existence of the pullback attractor for the three‐dimensional nonautonomous Camassa‐Holm system is proved in D(A1/2) and D(A).
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Random attractors for stochastic lattice reversible Gray-Scott systems with additive noise
Electronic Journal of Differential Equations, 2015 In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise.
Hongyan Li, Junyi Tu
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Global Mild Solutions and Attractors for Stochastic Viscous Cahn-Hilliard Equation
Abstract and Applied Analysis, 2011 This paper is devoted to the study of mild solutions for the initial and boundary value problem of stochastic viscous Cahn-Hilliard equation driven by white noise. Under reasonable assumptions we first prove the existence and uniqueness result.
Xuewei Ju +3 more
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Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics [PDF]
, 2020 An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\,x+p(t)$, where $q\colon\R\to\R$ and $p\colon\R\to\R$ are bounded and uniformly continuous, is fundamental to explain the absence ...
Longo, Iacopo Paolo +3 more
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Invariant manifolds as pullback attractors of nonautonomous differential equations
Discrete & Continuous Dynamical Systems - A, 2005 We discuss the relationship between invariant manifolds of nonautonomous differential equations and pullback attractors. This relationship is essential, e.g., for the numerical approximation of these manifolds. In the first step, we show that the unstable manifold is the pullback attractor of the differential equation.
Aulbach, Bernd +2 more
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Advances in Mathematical Physics, 2019 In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation.
Chunxiao Guo, Yanfeng Guo, Xiaohan Li
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Pullback attractor for N-dimensional thermoelastic coupled structure equations
Boundary Value Problems, 2018 In this paper, proving the pullback asymptotic compactness of processes by the aid of a contractive function in space X 0 $X_{0}$ , we prove the existence of a pullback attractor for N-dimensional nonautonomous thermoelastic coupled structure equations u
Danxia Wang, Yinzhu Wang
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