Time decay in dual-phase-lag thermoelasticity: Critical case

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Communications on Pure and Applied Analysis, ISSN: 1534-0392, Vol: 17, Issue: 1, Page: 177-190

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Ramón Quintanilla; Zhuangyi Liu
American Institute of Mathematical Sciences (AIMS)
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This note is devoted to the study of the time decay of the onedimensional dual-phase-lag thermoelasticity. In this theory two delay parameters τand τare proposed. It is known that the system is exponentially stable if τ< 2τ[22]. We here make two new contributions to this problem. First, we prove the polynomial stability in the case that τ= 2τas well the optimality of this decay rate. Second, we prove that the exponential stability remains true even if the inequality only holds in a proper sub-interval of the spatial domain, when τis spatially dependent.