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In this paper we investigate the spatial behavior of the solutions for\ud a theory for the heat conduction with one delay term. We obtain a Phragm én-\ud Lindelöf type alternative. That is, the solutions either decay in an exponential\ud way or blow-up at in nity in an exponential way. We also show how to obtain\ud an upper bound for the amplitude term. Later we point out how to extend\ud the results to a thermoelastic problem. We nish the paper by considering\ud the equation obtained by the Taylor approximation to the delay term. A\ud Phragm én-Lindelöf type alternative is obtained for the forward and backward\ud in time equations.Peer ReviewedPostprint (published version

This note is concerned with the linear (and linearised) type III thermoelastic theory\ud proposed by Green and Naghdi. First, the continuous dependence of the solutions upon\ud the initial data and supply terms is established for noncentrosymmetric bodies. Then a\ud uniqueness result for centrosymmetric materials is established.Peer ReviewedPostprint (published version

We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential stability for the Lord-Shulman model.

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