Continuous dependence for an implicit nonlinear equation
type: Item
instance of: scholarly article
title: Continuous dependence for an implicit nonlinear equation
zbMATH Open document ID: 0802.34074
author: Veli-Matti Hokkanen
published in: Journal of Differential Equations
publication date: 1994-07-04T00:00:00Z
review text: Consider the following problem: (1) \(v'(t)+ w(t)+ C(t)u(t)= f(t)\) for a.e. \(t\in (0,T)\), (2) \(v(t)\in A(t)u(t)\), \(w(t)\in B(t)u(t)\) for a.e. \(t\in (0,T)\), (3) \(v(0)= v_ 0\), where \(A(t)\) and \(B(t)\) are maximal monotone and linearly bounded operators in a real Hilbert space \(V\) and \(A(t)+ B(t)\) is \(V\)-coercive. Moreover, it is assumed that \(A(t)\) is the subdifferential of a continuous convex function on a real Banach space \(W\) and there exists a compact injection of \(V\) in \(W\). Apart from this \(C(t): V\to W^*\) is Lipschitzian. The object of the paper under review is the study of the continuous dependence of solutions of (1)--(3) on \(A\), \(B\), \(C\), \(f\) and \(v_ 0\). The results obtained are applied to control theory.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 599885
zbMATH Keywords: continuous dependence of solutions
reviewed by: Józef Banaś
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1060
OpenAlex ID: W1980573255
DOI: 10.1006/JDEQ.1994.1060
description: scientific article; zbMATH DE number 599885