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Dissipation rates and partition of energy in thermoelasticity. (English) Zbl 0563.73007
Partition of energy in the framework of the linear isotropic elasticity is examined; the equations of evolution consist of the three hyperbolic equations of motion (linear momentum) coupled with a parabolic equation of energy conservation. It is found that the rate of decay of energy is affected by the symmetry of the initial data measured by the orders of the lowest nonvanishing moments of the initial displacements, initial velocity, and initial temperature distribution. It is found among others that: (1) the strain energy is asymptotically equal to a convex combination of the kinetic and thermal energy; (2) in the asymptotic limit, and with no coupling, the results reduce to the known equipartition energy in elasticity; (3) total energy decays algebraically with the rate increasing with increasing symmetry of the initial data.
Reviewer: J.L.Nowinski

MSC:
74F05 Thermal effects in solid mechanics
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
74B99 Elastic materials
74A15 Thermodynamics in solid mechanics
35L05 Wave equation
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