Robustness of nonautonomous attractors for a family of nonlocal reaction–diffusion equations without uniqueness [PDF]
, 2015 In this paper, we consider a non-autonomous nonlocal reactiondiffusion equation with a small perturbation in the nonlocal diffusion term and the non-autonomous force.
Caraballo Garrido, Tomás +2 more
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Robustness of time-dependent attractors in H1-norm for nonlocal problems [PDF]
, 2018 In this paper, the existence of regular pullback attractors as well as their upper semicontinuous behaviour in H1-norm are analysed for a parameterized family of non-autonomous nonlocal reaction-diffusion equations without uniqueness, improving previous ...
Caraballo Garrido, Tomás +2 more
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Dynamics of wave equations with moving boundary [PDF]
, 2017 This paper is concerned with long-time dynamics of weakly damped semilinear wave equations defined on domains with moving boundary. Since the boundary is a function of the time variable the problem is intrinsically non-autonomous.
Ma, To Fu +2 more
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Attractors for processes on time-dependent spaces. Applications to wave equations [PDF]
, 2012 For a process U(t,s) acting on a one-parameter family of normed spaces, we present a notion of time-dependent attractor based only on the minimality with respect to the pullback attraction property. Such an attractor is shown to be invariant whenever the
Conti, Monica +2 more
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Pullback attractors for generalized evolutionary systems
Discrete & Continuous Dynamical Systems - B, 2015 We give an abstract framework for studying nonautonomous PDEs, called a generalized evolutionary system. In this setting, we define the notion of a pullback attractor. Moreover, we show that the pullback attractor, in the weak sense, must always exist. We then study the structure of these attractors and the existence of a strong pullback attractor.
Kavlie, Landon, Cheskidov, Alexey
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Pullback Attractors for Stochastic Young Differential Delay Equations [PDF]
Journal of Dynamics and Differential Equations, 2020 We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term which has no delay factor and has eigenvalues of negative real parts, then the generated random dynamical system ...
Cong, N., Luu, H., Hong, P.
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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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Parameter shifts for nonautonomous systems in low dimension: Bifurcation- and Rate-induced tipping [PDF]
, 2016 We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another.
Ashwin, Peter +2 more
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Weak topologies for Carath\'eodory differential equations. Continuous dependence, exponential Dichotomy and attractors [PDF]
, 2018 We introduce new weak topologies and spaces of Carath\'eodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields.
Longo, Iacopo P. +2 more
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On attractors, spectra and bifurcations of random dynamical systems [PDF]
, 2015 In this thesis a number of related topics in random dynamical systems theory are studied: local attractors and attractor-repeller pairs, the exponential dichotomy spectrum and bifurcation theory.
Callaway, Mark
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