Automatic control of the temperature in phase change problems with memory
type: Item
instance of: scholarly article
title: Automatic control of the temperature in phase change problems with memory
zbMATH Open document ID: 1027.35163
DOI: 10.4171/ZAA/1050
author: R. Smith
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2004-01-13T00:00:00Z
review text: The author deals with a parabolic two-phase system with memory occupying a bounded and smooth domain \(\Omega\subset \mathbb{R}^N\) \((N\geq 1)\), whose state is described by the pair \((\theta,\chi)\). Here \(\theta\) is the relative temperature \((\theta=0\) being the equilibrium temperature at which the two phases, for instance solid and liquid, can coexist) and \(\chi\) is the concentration of the more energetic phase (that is water in water-ice system). Assuming on the phase variable either a relaxation dynamics or a Stefan condition, the author proves existence and uniqueness results for feedback control problems corresponding to two different types of thermostat: the relay switch and the Preisach operator. Moreover, the author shows that, when the data enjoy suitable regularity properties, one can obtain a stronger regularity for the solution.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 35B37
Mathematics Subject Classification ID: 47J40
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1747395
zbMATH Keywords: parabolic two-phase system with memory
zbMATH Keywords: Preisach operator
zbMATH Keywords: regularity
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: feedback control problems
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1050
OpenAlex ID: W2012343981
description: scientific article; zbMATH DE number 1747395