We consider the system of dual-phase-lag thermoelasticity proposed by Chandrasekharaiah and Tzou. First, we prove that the solutions of the problem are generated by a semigroup of quasi-contractions. Thus, the problem of the third order in time is well-posed. Then the exponential stability is investigated. Finally the spatial behavior of solutions is analyzed in a semi-infinite cylinder and a result on the domain of influence is obtained.
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Quintanilla et al. (2006) studied this question.
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