On global attractors for a class of reaction-diffusion equations on unbounded domains with some strongly nonlinear weighted term
type: Item
instance of: scholarly article
title: On global attractors for a class of reaction-diffusion equations on unbounded domains with some strongly nonlinear weighted term
zbMATH Open document ID: 1418.35249
DOI: 10.1155/2015/251614
author: Jin Zhang
author: Chengkui Zhong
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: We consider the existence and properties of the global attractor for a class of reaction-diffusion equation \(\partial u / \partial t - \Delta u - u + \kappa(x) | u |^{p - 2} u + f(u) = 0\), in \(\mathbb{R}^n \times \mathbb{R}^+\); \(u(x, 0) = u_0(x)\), in \(\mathbb{R}^n\). Under some suitable assumptions, we first prove that the problem has a global attractor \(\mathcal{A}\) in \(L^2(\mathbb{R}^n)\). Then, by using the \(Z_2\)-index theory, we verify that \(\mathcal{A}\) is an infinite dimensional set and it contains infinite distinct pairs of equilibrium points.
Mathematics Subject Classification ID: 35K91
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 37L30
zbMATH DE Number: 7025278
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/251614
OpenAlex ID: W1548015178
Wikidata QID: Q59105724
cites work: Q4003101
cites work: Q4704642
cites work: Q3799008
cites work: Attractors for reaction-diffusion equations: existence and estimate of their dimension
cites work: Infinite-dimensional dynamical systems. An introduction to dissipative parabolic PDEs and the theory of global attractors
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
cites work: The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations
cites work: Attractors of partial differential evolution equations in an unbounded domain
cites work: Exponential attractors of reaction-diffusion systems in an unbounded domain
cites work: Global attractors for degenerate parabolic equations on unbounded domains
cites work: On the existence of the compact global attractor for semilinear reaction diffusion systems on \(\mathbb{R}^ N\)
cites work: Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains
cites work: Upper and lower bounds for the Kolmogorov entropy of the attractor for the RDE in an unbounded domain
cites work: Global attractors for the wave equation with nonlinear damping
cites work: The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov's \(\varepsilon\)-entropy
cites work: Q5708964
cites work: Attractors for reaction-diffusion equations in unbounded domains
cites work: On the \(Z_2\) index of the global attractor for a class of \(p\)-Laplacian equations
cites work: Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains
cites work: On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains
cites work: Pullback attractors for asymptotically compact non-autonomous dynamical systems
cites work: Q3645637
cites work: Pullback attractors for non-autonomous reaction-diffusion equations on \(\mathbb R^n\)
cites work: Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces
cites work: Q3997570
cites work: Q3336252
cites work: Q4186717
description: scientific article; zbMATH DE number 7025278