Extrapolation and inhomogeneous retarded differential equations on infinite dimensional spaces
type: Item
instance of: scholarly article
title: Extrapolation and inhomogeneous retarded differential equations on infinite dimensional spaces
zbMATH Open document ID: 0916.34065
DOI: 10.1007/BF02844372
author: A. Rhandi
author: Lahcen Maniar
publication date: 1999-07-12T00:00:00Z
review text: The authors study linear delay equations \[ \dot x(t) = Bx(t) + Lx_t + f(t),\quad x_0 = f \in C([-r,0],X), \] where \(X\) is a Banach space, \(B\) the generator of a strongly continuous semigroup on \(X\) and \(L\) a bounded linear operator from \(C([-r,0],X)\) into \(X\). Using extrapolation spaces they obtain, via an extrapolated semigroup on \(X \times C([-r,0],X)\) and the corresponding variation of parameters formula, unique mild solutions to the above problem.
reviewed by: Rainer Nagel
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 1203701
zbMATH Keywords: linear delay equations
zbMATH Keywords: extrapolation spaces
zbMATH Keywords: solutions
MaRDI profile type: Publication
cites work: Q4717177
cites work: Q4327845
cites work: Perturbation theory for dual semigroups. I. The sun-reflexive case
cites work: Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case
cites work: Q3776123
cites work: Q3308590
cites work: Theory of functional differential equations. 2nd ed
cites work: Q4342940
cites work: One-parameter semigroups of positive operators
cites work: Q4283331
cites work: The adjoint of a semigroup of linear operators
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Extrapolation methods to solve non-autonomous retarded partial differential equations
cites work: Positivity and stability for a population equation with diffusion on \(L^1\)
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 1203701