Uniqueness of the displacement-heat flux problem in thermoelasticity with two relaxation times
The classical theory of coupled thermoelasticity is described by equations that imply an infinite speed of thermoelastic disturbances in a body. In this paper the author considers two new thermoelastic theories which eliminate the infinite speed paradox: the theory derived by \textit{A. E. Green} and \textit{K. A. Lindsay} [(*) J. Elasticity 2, 1-7 (1972)] and the theory proposed by \textit{H. W. Lord} and \textit{Y. Shulman} [J. Mech. Phys. Solids 15, 299-309 (1967)]. First, an initial-boundary value problem in the theory derived by Green and Lindsay (*) is formulated in terms of displacement field and heat flux field. A uniqueness theorem is established. Then, the author shows that some of the field equations of one theory reduce to those of the other if the relaxation times satisfy some restrictions.
scientific article; zbMATH DE number 3926340