Heat Conduction Within Linear Thermoelasticity

J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth o...

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Main Author: Day, William A.
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: New York, NY Springer New York 1985, 1985
Edition:1st ed. 1985
Series:Springer Tracts in Natural Philosophy
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Preliminaries
  • §1.1 One-dimensional linear thermoelasticity
  • §1.2 An energy integral
  • 2 The Coupled and Quasi-static Approximation
  • §2.1 An integro-differential equation
  • §2.2 Construction of solutions
  • §2.3 Failure of the Maximum Principle
  • §2.4 Behaviour of the kernel
  • §2.5 Initial sensitivity to the boundary
  • §2.6 A monotone property of the entropy
  • 3 Trigonometric Solutions of the Integro-differential Equation
  • §3.1 Maximum Principles for the pointwise mean total energy density and the pointwise mean square heat flux
  • §3.2 The effect of coupling on trigonometric solutions
  • 4 Approximation by Way of the Heat Equation or the Integro-differential Equation
  • §4.1 Status of the heat equation
  • §4.2 Comments on Theorem 13
  • §4.3 Proof of Theorem 13
  • §4.4 Mean and recurrence properties of the temperature
  • §4.5 Status of the integro-differential equation
  • 5 Maximum and Minimum Properties of the Temperature Within the Dynamic Theory
  • §5.1 Maximum and minimum properties with prescribed heat fluxes
  • §5.2 Maximum and minimum properties with prescribed temperatures
  • References