The aim of the article is to review a number of results on finite wave speeds of thermoelastic disturbances that are based on two different models of a thermoelastic solid, and which were obtained mostly by the present author and his collaborators during the past 10 years. The two models discussed are the L–S model proposed, among others, by Lord and Shulman in 1967 and the G–L model introduced into the technical literature by Green and Lindsay in 1972. Each of the two models is a generalization of the classical one, and it has been introduced, among other reasons, in an attempt to eliminate the paradox of an infinite velocity of thermoelastic disturbances inherent in the classical model. A stress is made on the domain of influence theorems for arbitrary anisotropic and nonhomogeneous thermoelastic bodies in which the thermoelastic coupling cannot be ignored. Apart from the general results concerning the initial-boundary value problems in terms of various pairs of mechanical and thermal variables, some particular potential–temperature and one-dimensional results are discussed. The article should prove useful for those researchers who try to understand an effect of thermoelastic coupling on speed of thermoelastic waves in a nonhomogeneous and anisotropic medium as well as for those working on modeling of waves of more complex nature such as electromagneto-thermoelastic waves and others.

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