Flow invariance for nonautonomous nonlinear partial differential delay equations
type: Item
instance of: scholarly article
title: Flow invariance for nonautonomous nonlinear partial differential delay equations
zbMATH Open document ID: 1279.47093
author: Seyedeh Marzieh Ghavidel
author: Wolfgang M. Ruess
published in: Communications on Pure and Applied Analysis
publication date: 2013-06-06T00:00:00Z
review text: In this paper, the following nonautonomous partial differential delay equation \[ \left\{\begin{aligned} &\dot u(t)+B(t)u(t)\ni F(t,u_t), \quad 0\leq s\leq t,\\ &u_0=\phi, \end{aligned}\right. \] is considered, where the operators \(B(t)\subset X\times X\) are nonlinear and multivalued \(\omega\)-accretive operators in a Banach space \(X,\) \(\omega\in \mathbb R,\) \(\phi: I\to X,\) \(I=[-R,0]\) or \((-\infty,0],\) \(u_t(\theta)=u(t+\theta),\) \(\theta\in I.\) Several fundamental results on existence and flow-invariance of solutions are proved. The abstract results are applied to models from population dynamics.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 47J35
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 47N60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6171009
zbMATH Keywords: nonlinear partial differential delay equations
zbMATH Keywords: accretive operators
zbMATH Keywords: flow-invariance
zbMATH Keywords: population models
MaRDI profile type: Publication
full work available at URL: cpaa.2012.11.2351
OpenAlex ID: W2313924120
DOI: 10.3934/CPAA.2012.11.2351
description: scientific article; zbMATH DE number 6171009