Relaxation theorem for the evolution differential inclusions
type: Item
instance of: scholarly article
title: Relaxation theorem for the evolution differential inclusions
zbMATH Open document ID: 0940.34054
author: Wang Dong
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-12-05T00:00:00Z
review text: Let \(X\) be a separable Banach space, \(A\) the infinitesimal generator of a linear \(C_0\) semigroup on \(X\), \(F:[0,T] \times X\to X\) a set-valued map with nonempty compact convex values, and \(x_0\in X\). The author compares the solution sets to the differential inclusions \[ \dot x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr), \quad x(0)=x_0, \] and \[ \dot x(t)\in Ax(t)+ \text{ext} F \bigl(t,x(t)\bigr), \quad x(0)=x_0, \] where `\(\text{ext} F\)' denotes the set of extreme points of \(F\), and proves a density (relaxation) theorem. He seems to be unaware of earlier comparable results, that include the cases when \(A\) depends on time or is nonlinear. See, for instance, \textit{N. S. Papageorgiou} [Czech. Math. J. 44, No. 3, 481-500 (1994; Zbl 0868.34010); ibid., No. 4, 631-648 (1994; Zbl 0822.45008)].
Mathematics Subject Classification ID: 34G25
zbMATH DE Number: 1348144
zbMATH Keywords: evolution differential inclusions
reviewed by: Sergiu Aizicovici
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6473
OpenAlex ID: W2047269844
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DOI: 10.1006/JMAA.1999.6473
description: scientific article; zbMATH DE number 1348144