Positivity and stability for some partial functional differential equations
type: Item
instance of: scholarly article
title: Positivity and stability for some partial functional differential equations
zbMATH Open document ID: 1028.35150
author: Khalil Ezzinbi
author: Soumia Lalaoui Rhali
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2003-08-27T00:00:00Z
review text: The paper deals with the following partial functional-differential equation \[ u^\prime(t) = Bu(t) + F(u_t), \;t \geq 0, \] \[ u_0 = \varphi \in C([-r,0];X), \] where \(u_t (\theta) = u(t+\theta)\) for \(\theta \in [-r,0]\) and \(B\) is a non-densely defined linear operator satisfying the Hille-Yosida condition. The authors find necessary and sufficient conditions independent of the delay for the uniform exponential stability of the solution semigroup.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1971895
zbMATH Keywords: nondensely defined linear operator
zbMATH Keywords: partial functional differential equations
zbMATH Keywords: positivity
zbMATH Keywords: compactness
zbMATH Keywords: uniform exponential stability
reviewed by: Emil Minchev
MaRDI profile type: Publication
full work available at URL: s00030-003-1018-1
OpenAlex ID: W2040546603
DOI: 10.1007/S00030-003-1018-1
description: scientific article; zbMATH DE number 1971895