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Gradient-like parabolic semiflows on BUC(ℝN)


Daners, Daniel; Merino, Sandro (1998). Gradient-like parabolic semiflows on BUC(ℝN). Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 128(6):1281-1291.

Abstract

We prove that a class of weighted semilinear reaction diffusion equations on<jats:bold>R</jats:bold><jats:sup>N</jats:sup>generates gradient-like semiflows on the Banach space of bounded uniformly continuous functions on<jats:bold>R</jats:bold><jats:sup>N</jats:sup>. If<jats:italic>N</jats:italic>= 1 we show convergence to a single equilibrium. The key for getting the result is to show the exponential decay of the stationary solutions, which is obtained by means of a decay estimate of the kernel of the underlying semigroup.

Abstract

We prove that a class of weighted semilinear reaction diffusion equations on<jats:bold>R</jats:bold><jats:sup>N</jats:sup>generates gradient-like semiflows on the Banach space of bounded uniformly continuous functions on<jats:bold>R</jats:bold><jats:sup>N</jats:sup>. If<jats:italic>N</jats:italic>= 1 we show convergence to a single equilibrium. The key for getting the result is to show the exponential decay of the stationary solutions, which is obtained by means of a decay estimate of the kernel of the underlying semigroup.

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Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:1 January 1998
Deposited On:23 Oct 2018 16:55
Last Modified:31 Jul 2020 02:04
Publisher:Cambridge University Press
ISSN:0308-2105
OA Status:Green
Publisher DOI:https://doi.org/10.1017/s0308210500027323
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101017S0308210500027323 (Library Catalogue)

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