Properties of the solution set of nonlinear evolution inclusions
type: Item
instance of: scholarly article
title: Properties of the solution set of nonlinear evolution inclusions
zbMATH Open document ID: 0879.34018
DOI: 10.1007/BF02683335
author: Nikolaos S. Papageorgiou
author: Nazeer Shahzad
published in: Applied Mathematics and Optimization
publication date: 1998-01-19T00:00:00Z
review text: The paper deals with nonlinear nonautonomous evolution inclusions of the form \[ \dot x(t)+ A(t,x(t)) \in F(t,x(t)), \] a.e. on \(T\), \(x(0) =x_0\) defined on a Gelfand triple of spaces \((X,H,X^*)\). In Section 3 the authors provide conditions for the solution set to be an \(R_\delta\)-set, or path-connected in \(C(T,H)\). An invariance result is given in Section 4, together with a result on the existence of periodic solutions. In the last section applications of these results are given for some parabolic partial differential equations with multivalued terms.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 35R70
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1047002
zbMATH Keywords: nonlinear nonautonomous evolution inclusions
zbMATH Keywords: Gelfand triple
zbMATH Keywords: periodic solutions
zbMATH Keywords: parabolic partial differential equations
reviewed by: George Karakostas
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02683335
OpenAlex ID: W2081480602
description: scientific article; zbMATH DE number 1047002