Resolvents of operators and partial functional differential equations with nonautonomous past.
type: Item
instance of: scholarly article
title: Resolvents of operators and partial functional differential equations with nonautonomous past.
zbMATH Open document ID: 1063.47033
author: Nguyen Thieu Huy
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-26T00:00:00Z
review text: In this paper, for an abstract differential operator \(G\) corresponding to the integral equation \(u(t)=U(t,s)u(s)+\int_t^sU(t\xi)f(\xi)d\xi\) on a Banach space of \(X\)-valued functions on \({\mathbb{R}_-}\), where \(U(t,s)\) belongs to a backward evolution family, the author computes the resolvent of its restriction to a smaller domain to obtain a generator. By using these results, the author further proves existence, exponential stability and exponential dichotomy of solutions to a partial functional equation with nonautonomous past.
reviewed by: Shihuang Hong
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 2032972
zbMATH Keywords: functional differential equations
zbMATH Keywords: evolution semigroups
zbMATH Keywords: resolvents of operators
zbMATH Keywords: existence of solutions
zbMATH Keywords: exponential stability
zbMATH Keywords: exponential dichotomy
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.09.060
OpenAlex ID: W2008095897
cites work: PFDE with nonautonomous past
cites work: Q4258125
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Weak spectral mapping theorems for functional differential equations
cites work: Introduction to functional differential equations
cites work: Exponentially dichotomous operators and exponential dichotomy of evolution equations on the half-line
cites work: An integrability condition on the resolvent for hyperbolicity of the semigroup
cites work: Analytic semigroups and optimal regularity in parabolic problems
cites work: On the proof of characterizations of the exponential dichotomy
cites work: Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
cites work: Characterizations of dichotomies of evolution equations on the half-line
cites work: Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces
cites work: The asymptotic behaviour of semigroups of linear operators
cites work: Non-autonomous Miyadera perturbations
cites work: Extrapolation methods to solve non-autonomous retarded partial differential equations
cites work: On Positive Contractions In L p -Spaces
cites work: Asymptotically autonomous parabolic evolution equations.
DOI: 10.1016/J.JMAA.2003.09.060
Recommended article: Q3336104
Recommended article: On the resolvent of linear nonautonomous partial functional differential equations
Recommended article: Resolvent Operators for Some Classes of Integro-Differential Equations
Recommended article: Resolvent operators and weak solutions of integrodifferential equations
Recommended article: Partial functional differential equations with nonautonomous past in \(L^ p\)-phase spaces.
Recommended article: On resolvents of intergral and partially integral operators
Recommended article: Resolvent of nonautonomous linear delay functional differential equations
Recommended article: A generalization of resolvent families of operators
Recommended article: Resolvent operator for abstract functional differential equations with infinite delay
Recommended article: Существование близких псевдоголоморфных дисков для почти комплексных многообразий и приложение к псевдонорме Кобаяси - Ройдена
description: scientific article; zbMATH DE number 2032972