Positivity and regularity of hyperbolic Volterra equations in Banach spaces
type: Item
instance of: scholarly article
title: Positivity and regularity of hyperbolic Volterra equations in Banach spaces
zbMATH Open document ID: 0608.45007
DOI: 10.1007/BF01461726
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164325
review text: We derive necessary and sufficient conditions for two classes of linear Volterra equations of the form (*) \(u=f+a*Au\) to admit finite wave speed as well as continuity across the wave front. These conditions are based on the positivity of the fundamental solution. One of these classes serves as a model in linear viscoelasticity. These results are then used to obtain several general theorems on existence, positivity, regularity and asymptotic behavior of the resolvent for (*).
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 74D99
zbMATH DE Number: 3983845
zbMATH Keywords: hyperbolic Volterra equations
zbMATH Keywords: Banach spaces
zbMATH Keywords: linear viscoelasticity
zbMATH Keywords: existence
zbMATH Keywords: positivity
zbMATH Keywords: regularity
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: resolvent
author: Jan Pruess
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3983845