scholarly journals Intrinsic Shape Property of Global Attractors in Metrizable Spaces

2020 ◽  
Vol 16 (1) ◽  
pp. 181-194
Author(s):  
N. Shekutkovski ◽  
◽  
M. Shoptrajanov ◽  
Keyword(s):  
Global Attractors ◽  
Intrinsic Shape ◽  
Shape Property ◽  
Metrizable Spaces

scholarly journals Pointed shape and global attractors for metrizable spaces

2011 ◽  
Vol 158 (2) ◽  
pp. 167-176 ◽  
Author(s):  
A. Giraldo ◽  
R. Jiménez ◽  
M.A. Morón ◽  
F.R. Ruiz del Portal ◽  
J.M.R. Sanjurjo
Keyword(s):  
Global Attractors ◽  
Metrizable Spaces

Universal elements for families of separable metrizable spaces

1998 ◽  
Vol 91 (6) ◽  
pp. 3387-3415
Author(s):  
D. N. Georgiou ◽  
S. D. Iliadis
Keyword(s):  
Metrizable Spaces

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract 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. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

scholarly journals The apparent and intrinsic shape of the APM galaxy clusters

2000 ◽  
Vol 316 (4) ◽  
pp. 779-785 ◽  
Author(s):  
S. Basilakos ◽  
M. Plionis ◽  
S. J. Maddox
Keyword(s):  
Galaxy Clusters ◽  
Intrinsic Shape

scholarly journals Asymptotic Smoothing and Global Attractors for a Class of Nonlinear Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yongqin Xie ◽  
Zhufang He ◽  
Chen Xi ◽  
Zheng Jun
Keyword(s):  
Evolution Equations ◽  
Global Solutions ◽  
Global Attractors ◽  
Nonlinear Evolution Equations ◽  
Time Behavior ◽  
Asymptotic Regularity ◽  
Compact Attractor ◽  
Long Time ◽  
Critical Exponential Growth ◽  
Semilinear Evolution Equations

We prove the asymptotic regularity of global solutions for a class of semilinear evolution equations in H01(Ω)×H01(Ω). Moreover, we study the long-time behavior of the solutions. It is proved that, under the natural assumptions, these equations possess the compact attractor 𝒜 which is bounded in H2(Ω)×H2(Ω), where the nonlinear term f satisfies a critical exponential growth condition.

Optimal metrics on metrizable spaces

1971 ◽  
Vol 22 (1) ◽  
pp. 660-663
Author(s):  
Ludvik Janos
Keyword(s):  
Metrizable Spaces
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