Nonlinear semigroup of a class of abstract semilinear functional-differential equations with a non-dense domains
type: Item
instance of: scholarly article
title: Nonlinear semigroup of a class of abstract semilinear functional-differential equations with a non-dense domains
zbMATH Open document ID: 1081.34076
author: Mostafa Adimy
author: Mostafa Laklach
author: Khalil Ezzinbi
publication date: 2005-06-07T00:00:00Z
review text: Let \(A\) be a Hille-Yosida operator with non-dense domain in a Banach space \(X\). Here, the abstract semilinear autonomous functional-differential equation \[ \overset{\cdot}{u}(t)=Au(t)+F(u_{t}), \quad t>0,\;u_{0}=\varphi, \] is considered. Let \(\{ U( t) :t\geq0\} \) be the family of nonlinear operators defined on \[ Y=\{ \varphi\in C([ -r,0] ,X) :\varphi(0) \in\overline{D(A)}\} \] by \[ U( t) =u_{t} (\cdot,\varphi) \] for \(t\geq0\) and \(\varphi\in Y\). In case \(F\) is globally Lipschitzian, \(\{ U( t) :t\geq0\} \) defines a nonlinear strongly continuous semigroup of continuous operators on \(Y\). Using the Crandall-Liggett approach, the authors study the semigroup \(\{ U( t) :t\geq0\} \).
reviewed by: Nazim Idrisoglu Mahmudov
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 2174206
zbMATH Keywords: nonlinear semigroup
zbMATH Keywords: semilinear functional-differential equation
zbMATH Keywords: Hille-Yosida operator
zbMATH Keywords: Crandall-Liggett approach
MaRDI profile type: Publication
full work available at URL: s10114-004-0341-3
OpenAlex ID: W2161872089
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DOI: 10.1007/S10114-004-0341-3
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2174206