On the convergence of hyperbolic semigroups in variable Hilbert spaces
type: Item
instance of: scholarly article
title: On the convergence of hyperbolic semigroups in variable Hilbert spaces
zbMATH Open document ID: 1126.47038
author: Svetlana E. Pastukhova
published in: Journal of Mathematical Sciences (New York)
publication date: 2007-08-07T00:00:00Z
review text: Resolvent convergence is considered for nonnegative selfadjoint operators acting in variable Hilbert spaces \(H_{\varepsilon}\). The limit of the resolvents is, generally, a ``pseudoresolvent'' and not a resolvent. The situation may occur even for \(H_{\varepsilon}\equiv H\). This convergence is used for passing to the limit in the corresponding hyperbolic differential-operator equations in \(H_{\varepsilon}\) considered from the semigroup point of view. The scheme studied in the paper can be applied to the homogenization of nonstationary problems of elasticity for thin structures.
reviewed by: Yakov Yakubov
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 5177654
zbMATH Keywords: resolvent convergence
zbMATH Keywords: pseudo-resolvent
zbMATH Keywords: hyperbolic semigroup
zbMATH Keywords: hyperbolic operator equation
zbMATH Keywords: elasticity
MaRDI profile type: Publication
full work available at URL: s10958-005-0178-z
OpenAlex ID: W2016713907
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DOI: 10.1007/S10958-005-0178-Z
description: scientific article; zbMATH DE number 5177654