On the existence of the compact global attractor for semilinear reaction diffusion systems on \(\mathbb{R}^ N\)
type: Item
instance of: scholarly article
title: On the existence of the compact global attractor for semilinear reaction diffusion systems on \(\mathbb{R}^ N\)
zbMATH Open document ID: 0867.35045
author: Sandro Merino
published in: Journal of Differential Equations
publication date: 1996-01-01T00:00:00Z
review text: In this interesting paper, the author considers abstract parabolic systems of the form \[ \partial_tu_k+A_k(x,\partial)u_k=f_k(x,u), \] where \(u=(u_1,\dots,u_k)\) is a function of \(t\) and \(x\in\mathbb{R}^N\). A typical example is an equation with a potential: \(u_t-\Delta u=m(x)u-u^3\). The space, the solution is looked for, is the space of bounded uniformly continuous functions. According to the properties of the potential \(m\), the corresponding semiflow can be compact and, consequently, the global compact attractor exists. Sufficient conditions for the Hausdorff dimension of the attractor to be finite are also discussed.
reviewed by: Eduard Feireisl
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 952551
zbMATH Keywords: abstract parabolic systems
zbMATH Keywords: Hausdorff dimension
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0172
OpenAlex ID: W2022065221
DOI: 10.1006/JDEQ.1996.0172
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description: scientific article; zbMATH DE number 952551