Long-term analysis of degenerate parabolic equations in \(\mathbb R^N\)
type: Item
instance of: scholarly article
title: Long-term analysis of degenerate parabolic equations in \(\mathbb R^N\)
zbMATH Open document ID: 1317.35133
author: Gaocheng Yue
author: Chengkui Zhong
publication date: 2015-03-25T00:00:00Z
review text: The authors establish that the solution semigroup of \[ \partial_t u-\sum_{i=1}^N\partial_{x_i}\bigl(\left| \partial_{x_i}\right|^{p-2}\partial_{x_i}\bigr)+f(u)=g(x), \qquad x\in{\mathbb R}^N \] has a \((L^2_U({\mathbb R}^N),L^2_{\text{loc}}({\mathbb R}^N))\)-global attractor in case that \(p>2\), \(g\in L^2_U({\mathbb R}^N)\), \(f\in C({\mathbb R}^N,{\mathbb R}^N)\), \(f(0)=0\), \(f\) has polynomial growth, and satisfies certain local Lipschitz-type and monotonicity-type conditions. They also give an estimate for the Kolmogorov \(\epsilon\)-entropy of the attractor. The work is based on the \(l\)-trajectory method.
reviewed by: Georg Hetzer
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 6419645
zbMATH Keywords: degenerate parabolic equations
zbMATH Keywords: unbounded domain
zbMATH Keywords: locally uniform spaces
zbMATH Keywords: global attractor
zbMATH Keywords: Kolmogorov \(\epsilon\)-entropy
zbMATH Keywords: \(l\)-trajectory method
MaRDI profile type: Publication
full work available at URL: s10114-015-4178-8
OpenAlex ID: W2068061152
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DOI: 10.1007/S10114-015-4178-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6419645