Stochastic representation of partial differential inclusions
type: Item
instance of: scholarly article
title: Stochastic representation of partial differential inclusions
zbMATH Open document ID: 1178.60049
author: Michał Kisielewicz
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-13T00:00:00Z
review text: Partial differential inclusions of the form \(u_t^\prime \in \mathbb L _{FG}u+cu\) and \(\psi \in \mathbb L_{FG}u+cu\), where \(\mathbb L_{FG}\) is a uniformly parabolic second order set-valued operator, are considered. In particular, based on diffusions properties of weak solutions to stochastic differential inclusions, some existence and representation theorems for solutions of such type partial differential inclusions are given. Partial differential inclusions are investigated together with some initial and boundary conditions. The presented approach leads to natural methods of solving some optimal control problems for systems described by partial differential equations depending on control parameters.
reviewed by: Elisa Alòs
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 5553639
zbMATH Keywords: Partial differential inclusions
zbMATH Keywords: stochastic differential inclusions
zbMATH Keywords: optimal control
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.12.022
OpenAlex ID: W1999697040
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DOI: 10.1016/J.JMAA.2008.12.022
description: scientific article; zbMATH DE number 5553639