Results 41 to 50 of about 4,947,310 (278)
Existence and attractors of solutions for nonlinear parabolic systems
Electronic Journal of Qualitative Theory of Differential Equations, 2001 We prove existence and asymptotic behaviour results for weak solutions of a mixed problem (S). We also obtain the existence of the global attractor and the regularity for this attractor in $\left[H^{2}(\Omega )\right] ^{2}$ and we derive estimates of its
Hamid El Ouardi, Abderrahmane El Hachimi
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Mathematical Biosciences and Engineering, 2020 In this paper we introduce a method of global exponential attractor in the reaction-diffusion epidemic model in spatial heterogeneous environment to study the spread trend and long-term dynamic behavior of the COVID-19 epidemic.
Cheng-Cheng Zhu, Jiang Zhu
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Global attractor for a strongly damped wave equation with fully supercritical nonlinearities
, 2016 The paper investigates the existence of global attractor for a strongly damped wave equation with fully supercritical nonlinearities: \begin{document}$ u_{tt}-Δ u- Δu_t+h(u_t)+g(u)=f(x) $\end{document} .
Zhijian Yang, Zhiming Liu
semanticscholar +1 more source
Finite-dimensional global attractors in Banach spaces
Journal of Differential Equations, 2010 We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic ...
Carvalho, Alexandre Nolasco +2 more
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Bifurcations, robustness and shape theory of attractors of discrete dynamical systems [PDF]
Journal of Fixed Point Theory and Applications volume 22, Article
number: 29 (2020), 2018 We study in this paper global properties, mainly of topological nature, of attractors of discrete dynamical systems. We consider the Andronov-Hopf bifurcation for homeomorphisms of the plane and establish some robustness properties for attractors of such homeomorphisms.
arxiv +1 more source
Attractors for a class of doubly nonlinear parabolic systems
Electronic Journal of Qualitative Theory of Differential Equations, 2006 In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in $\left[ L^{\infty }(\Omega )\right] ^{2 ...
Hamid El Ouardi, Abderrahmane El Hachimi
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Dynamic of the nonclassical diffusion equation with memory
Boundary Value Problems, 2023 In this paper, we consider the nonclassical diffusion equation with memory and the nonlinearity of the polynomial growth condition of arbitrary order in the time-dependent space.
Jing Wang +3 more
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Stability of limit regimes in general reaction-diffusion type systems
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2022 In this paper, we consider the stability of limit regimes for a general class of nonlinear distributed mathematical models named Reaction-Diffusion models. RD systems naturally arise in many applications.
О. В. Капустян +1 more
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On the Strength of Attractors in a High-dimensional System: Milnor Attractor Network, Robust Global Attraction, and Noise-induced Selection [PDF]
, 1998 Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase. Such dominance of fragile attractors is understood by robustness of global attraction in the phase space.
arxiv +1 more source
Shadowing in non-compact spaces with a global attractor [PDF]
arXiv, 2023 This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in certain types of dynamical systems in non-compact spaces if and only if $K$ is trivial.
arxiv