Steady-state problems of nonlinear electro-magneto-thermo-elasticity
type: Item
instance of: scholarly article
title: Steady-state problems of nonlinear electro-magneto-thermo-elasticity
zbMATH Open document ID: 0633.73108
DOI: 10.1007/BF00276839
author: Robert C. Rogers
author: Stuart S. Antman
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: In this paper, steady state problems in nonlinear electro-magneto-thermo- elasticity are studied. In part I of the paper, the governing equations, constitutive equations, and boundary conditions are treated. Use is made of strong ellipticity condition in place of Clausius-Duhem inequality. Some general existence theorems in two cases, namely (i) conservative systems and (ii) rigid conductors are stated and proved. In part II, some semi-inverse problems are formulated for a cylindrical tube and the consequences of strong ellipticity and growth conditions are discussed. Existence of classical solutions to certain boundary-value problems when the strong ellipticity and growth conditions hold is proved. Methods and notations of functional analysis are used throughout the above discussions. The paper will be definitely of interest to those seeking the applications of functional analysis to physical problems.
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 4031196
zbMATH Keywords: steady state problems
zbMATH Keywords: nonlinear electro-magneto-thermo-elasticity
zbMATH Keywords: governing equations
zbMATH Keywords: constitutive equations
zbMATH Keywords: boundary conditions
zbMATH Keywords: strong ellipticity condition
zbMATH Keywords: Clausius-Duhem inequality
zbMATH Keywords: existence theorems
zbMATH Keywords: conservative systems
zbMATH Keywords: rigid conductors
zbMATH Keywords: semi-inverse problems
zbMATH Keywords: cylindrical tube
zbMATH Keywords: growth conditions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00276839
OpenAlex ID: W2012514878
description: scientific article; zbMATH DE number 4031196