*-solutions of evolution equations in Hilbert space
type: Item
instance of: scholarly article
title: *-solutions of evolution equations in Hilbert space
zbMATH Open document ID: 0613.34048
DOI: 10.1016/0022-0396(87)90172-0
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: The paper gives sufficient conditions under which ''variation-of- constants'' solutions of semilinear evolution equations in a Hilbert space \(u'(t)=A(t)u(t)+g(u,t)\) are ''*-solutions'', i.e. solutions of \[ (u(t)- u(s),y)=\int^{t}_{s}((u(\sigma),A^*(\sigma)y)+(g(u,\sigma),y))d\sigma \] for all \(0\leq s<t\leq T\) and all \(y\in D=\cap_{0\leq t\leq T}D(A(t))\), assuming that this set is dense, and under which these two notions of solutions are equivalent. The case where D is not dense is also treated. As a motivation, the authors mention a class of stochastic evolution equations.
reviewed by: Hans Engler
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 3991967
zbMATH Keywords: mild solutions
zbMATH Keywords: weak solutions
zbMATH Keywords: semilinear evolution equations
zbMATH Keywords: Hilbert space
zbMATH Keywords: stochastic evolution equations
author: Donald A. Dawson
author: Luis G. Gorostiza
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90172-0
OpenAlex ID: W2036612197
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description: scientific article; zbMATH DE number 3991967