ON THE ASYMPTOTIC PARTITION OF ENERGY IN LINEAR THERMOELASTICITY

The author considers the classical linear theory of thermoelasticity for inhomogeneous and anisotropic materials. He investigates the asymptotic partition of total energy for the solutions of the initial boundary value problems of linear thermoelasticity. He materializes the idea of partition in terms of the asymptotic behavior in the Cesaro sense of various parts of the total energy associated to a solution. Thus he proves, among other things, that the mean thermal energy tends to zero as time goes to infinity. The author demonstrates that the asymptotic equipartition occurs between the Cesaro means of the kinetic and strain energies. This proves that thermal effects do not influence explicitly the asymptotic equipartition of the mean kinetic and strain energies. Therefore, the result established by W. A. Day for linear elastodynamics continues to hold in the framework of dynamic linear thermoelasticity.