Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface
type: Item
instance of: scholarly article
title: Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface
zbMATH Open document ID: 0723.73017
DOI: 10.1007/BF01041068
author: Morton E. Gurtin
author: S. B. Angenent
published in: Archive for Rational Mechanics and Analysis
publication date: 1989-01-01T00:00:00Z
review text: Among the results of \textit{M. E. Gurtin}'s paper [see this Zbl 0723.73016] on the thermodynamics of two-phase rigid continua based on Gibbs's notion of sharp phase-interface endowed with energy, entropy, and superficial force we remained those regarding the exact and approximate free boundary conditions at the interface and a hierarchy of free boundary problems. These problem are extremely difficult to solve because of nonlinearities inherent in the free boundary conditions. In the case of perfrect conductors, i.e. materials with infinite thermal conductivity, the temperature is constant and the corresponding free boundary problem reduces to a single set of evolution equations for interfaces. The goal of this paper is the theory of rigid perfect conductors with interfaces that evolve as curves in \({\mathbb{R}}2\). The paper contains a lot of results of great interest regarding the evolution of an isothermal interface. To form an idea of the problems treated in this paper we present its main sections. I. The thermodynamics of evolving curves, II. Smooth interfacial motions, III. Interfacial motions with corners, and IV. Nonsmooth interfacial energies.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 80A17
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 4193212
zbMATH Keywords: evolution equations for interfaces
zbMATH Keywords: rigid perfect conductors
zbMATH Keywords: thermodynamics of evolving curves
zbMATH Keywords: Smooth interfacial motions
zbMATH Keywords: Interfacial motions with corners
zbMATH Keywords: Nonsmooth interfacial energies
reviewed by: Gheorghe Gr. Ciobanu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4193212