Non-isothermal phase transition models with Neumann boundary conditions.
type: Item
instance of: scholarly article
title: Non-isothermal phase transition models with Neumann boundary conditions.
zbMATH Open document ID: 1036.35068
DOI: 10.1016/S0362-546X(03)00032-4
author: Akio Ito
author: Nobuyuki Kenmochi
author: M. Kubo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-07-01T00:00:00Z
review text: The Penrose-Fife system is a model of phase transitions which describes the space-time evolution of the absolute temperature \(u>0\) and the order parameter \(w\) (which is the state variable characterizing the phase). This system couples a second-order parabolic equation for \(u\) to a second-order (non-conserved case) or a fourth-order (conserved case) parabolic variational inequality for \(w\). For the heat flux \(\mathbf{q}=\nabla(1/u)\), several existence and uniqueness results have already been obtained for the mixed boundary condition \(\partial_\nu(1/u) + n_0 (1/u) = 0\) for the inverse temperature \(1/u\) with \(n_0>0\). These results are extended here to homogeneous Neumann boundary conditions \(\partial_\nu(1/u)=0\) (\(n_0=0\)) for the inverse temperature.
reviewed by: Philippe Laurençot
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K85
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 74N99
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 1945015
zbMATH Keywords: Penrose-Fife model
zbMATH Keywords: order parameter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1945015