Differential inclusions with nonstationary maximal monotone operators
type: Item
instance of: scholarly article
title: Differential inclusions with nonstationary maximal monotone operators
zbMATH Open document ID: 0722.34012
DOI: 10.1007/BF01077331
author: D. Kharzeev
publication date: 1990-01-01T00:00:00Z
review text: The paper deals with the differential equation (1) \(\dot x(t)+A^ tx(t)=0\), \(x(0)=x_ 0\in \overline{D(A^ 0)}\) in a Hilbert space H, where \(A^ t: D(A^ t)\to 2^ X\) is a time dependent maximal monotone multivalued operator, \(D(A^ t)\subset H\), \(t\in [0,T]\). For maximal monotone operators \(A_ 1\), \(A_ 2\) the author defines a distance \(d(A_ 1,A_ 2)\) (which is not a metric) and studies its properties. The main result is the proof of existence and uniqueness of problem (1) for an arbitrary regular operator \(A^ t\) (0\(\leq t\leq T)\). The operator \(A^ t\) is said to be regular if a) \(A^ t\) is maximal and monotone for \(0\leq t\leq T\), b) int D(A\({}^ t)\neq \emptyset\) for \(0\leq t\leq T\), c) the map \(t\to A^ t\) is continuous with respect to the distance d.
reviewed by: Irena Rachůnková
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 4190167
zbMATH Keywords: differential inclusion
zbMATH Keywords: time dependent maximal monotone multivalued operator
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: Functional evolution equations involving time dependent maximal monotone operators in Banach spaces
cites work: Evolution problem associated with a moving convex set in Hilbert space
cites work: Q3704500
cites work: Stochastic differential equations with reflecting boundary condition in convex regions
cites work: Perturbations of regularizing maximal monotone operators
full work available at URL: https://doi.org/10.1007/bf01077331
OpenAlex ID: W2081693790
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4190167