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Lyapunov Functions for Thermomechanics with Spatially Varying Boundary Temperatures

  • J. M. Ball
  • G. Knowles

Abstract

Consider a continuous body subjected to conservative body and surface forces, with a part ∂Ω 2 of the boundary maintained at a temperature θ = θ 0(X) and with the remainder of the boundary thermally insulated. A calculation of Duhem [1911] shows that if θ 0 is constant then the equations of motion possess a Lyapunov function, the equilibrium free energy, given in a standard notation (see Section 2) by
$$E = athop {nt ll }imits_mega Reft( {rac{1}{2}{{eft| psilon ight|}^2} + U + si - {heta _0}ta } ight)dX - athop {nt {{t_R} dot xdA.} }imits_{artial mega ackslash artial {mega _1}} $$
(1.1)

Keywords

Lyapunov Function Reference Configuration Free Energy Function Continuous Body Heat Flux Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • J. M. Ball
    • 1
    • 2
  • G. Knowles
    • 1
    • 2
  1. 1.Department of MathematicsHeriot-Watt UniversityEdinburghScotland
  2. 2.Department of Electrical EngineeringImperial College of Sciene and TechnologyLondonUK

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