Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory
type: Item
instance of: scholarly article
title: Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory
zbMATH Open document ID: 0897.45012
author: Pierluigi Colli
author: Jürgen Sprekels
published in: Journal of Differential Equations
publication date: 1998-07-30T00:00:00Z
review text: The authors consider a phase-field model of Penrose-Fife type in which the heat flux contains two distinct parts: one part that is proportional to the spatial gradient of the inverse temperature, and another one that depends on the past history of the temperature gradient. The main result of the paper is concerned with the existence and uniqueness of weak (variational) solutions to an initial-boundary value problem for a system of integro-partial differential equations describing the above model. The approach is based on the study of a related approximating problem, followed by passage to the limit. This requires establishing delicate estimates for the approximate solutions. Although the analysis is completed for a bounded three-dimensional domain, it is conjectured that the theory holds in any spatial dimension.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 1130543
zbMATH Keywords: weak solution
zbMATH Keywords: Penrose-Fife phase-field systems
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: system of integro-partial differential equations
reviewed by: Sergiu Aizicovici
MaRDI profile type: Publication
full work available at URL: jdeq.1997.3344
OpenAlex ID: W2011711739
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DOI: 10.1006/JDEQ.1997.3344
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description: scientific article; zbMATH DE number 1130543