Long time asymptotics of fourth order parabolic equations
type: Item
instance of: scholarly article
title: Long time asymptotics of fourth order parabolic equations
zbMATH Open document ID: 0851.35018
DOI: 10.1007/BF02787796
published in: Journal d'Analyse Mathématique
publication date: 1996-04-28T00:00:00Z
review text: The development of the spectral properties for parabolic equations associated with higher-order elliptic operators is quite different from the corresponding second-order operators. In particular, the long time behaviour of solutions can be strikingly different from what one is familiar with for second-order ones. The paper shows that long time growth of the semigroup generated by a fourth-order elliptic operator can occur even for constant coefficients operator. Two different examples of such operators are given. On the other hand also an example of a constant coefficient operator in one dimension which generates a semigroup bounded in time is exhibited. A detailed study of the long time asymptotics in one dimension is made; the generalization of results to higher space dimensions and more complicated operators remains an open problem.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 871568
zbMATH Keywords: long time growth of the semigroup
author: E. Brian Davies
reviewed by: S. Totaro
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 871568