On the structure of the solution set of evolution inclusions with time-dependent subdifferentials
type: Item
instance of: scholarly article
title: On the structure of the solution set of evolution inclusions with time-dependent subdifferentials
zbMATH Open document ID: 0893.34060
author: Francesca Papalini
author: Nikolaos S. Papageorgiou
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1998-08-24T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108420
review text: The Cauchy problem \[ \begin{gathered} -x'(t)\in \partial \varphi\bigl(t, x(t)\bigr) +F \bigl(t,x(t) \bigr),\;t\in T=[0,b], \\ x(0)=\xi, \tag{P} \end{gathered} \] is considered in a real separable Hilbert space \(H\). Here \(\xi\in H\), \(\varphi: T\times H \to(-\infty, \infty]\) is proper, convex and lower semicontinuous on \(H\) for each fixed \(t\), and satisfies a time-dependence condition of \textit{S. Yotsutani} type [J. Math. Soc. Japan 31, 623-646 (1978; Zbl 0414.35041)], while the multifunction \(F:T\times H\to 2^H\) is assumed to be closed valued. The authors first discuss the nonemptiness and the topological structure of the solution set of (P) when \(\varphi(t,.)\) is of compact type for every \(t\in T\), and \(F\) has convex values. The study is then extended to the case when \(F\) is no longer convex-valued and the functions \(\varphi(t,.)\) are not necessarily of compact type. Some examples involving parabolic distributed parameter systems are also presented.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 1089776
zbMATH Keywords: evolution inclusions
zbMATH Keywords: subdifferentials
zbMATH Keywords: Cauchy problem
zbMATH Keywords: parabolic
zbMATH Keywords: systems
reviewed by: Sergiu Aizicovici
MaRDI profile type: Publication
cites work: Aronszajn's theorem for a parabolic partial differential equation
cites work: Q4094029
cites work: Extensions and selections of maps with decomposable values
cites work: Q5665783
cites work: On the set of solutions to Lipschitzian differential inclusions
cites work: Characterizations of certain classes of semicontinuous multifunctions by continuous approximations
cites work: Q3688675
cites work: Non-convex-valued differential inclusions in Banach spaces
cites work: Topological properties of nonconvex differential inclusions
cites work: Topological properties of nonconvex differential inclusions of evolution type
cites work: Measurable relations
cites work: A note on the solution sets of differential inclusions
cites work: On the properties of the solution set of semilinear evolution inclusions
cites work: On the topological regularity of the solution set of differential inclusions with constraints
cites work: On decreasing sequences of compact absolute retracts
cites work: Some nonlinear parabolic variational inequalities
cites work: Q4172364
cites work: Convergence theorems for Banach space valued integrable multifunctions
cites work: Q3772448
cites work: Q4032545
cites work: Q4873135
cites work: Discontinuous Semilinear Differential Equations and Multiple Valued Maps
cites work: Survey of Measurable Selection Theorems
cites work: Q4112274
cites work: Evolution equations associated with the subdifferentials
description: scientific article; zbMATH DE number 1089776