This note is devoted to the study of the time decay of the onedimensional dual-phase-lag thermoelasticity. In this theory two delay parameters τq and τθ are proposed. It is known that the system is exponentially stable if τq < 2τθ . We here make two new contributions to this problem. First, we prove the polynomial stability in the case that τq = 2τθ as 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 τθ is spatially dependent.
Bibliographical noteFunding Information:
2000 Mathematics Subject Classification. Primary: 35Q70, 35B40; Secondary: 74F05. Key words and phrases. Phase-lag, thermoelasticity, polynomial stability, exponential stability. The second author R. Q. is supported by the Projects “Análisis Matemático de las Ecuaciones en Derivada Parciales de la Termomecánica“(MTM2013-42004-P), “Análisis Matemático de Pro-blemas de la Termomecánica“(MTM2016-74934-P), (AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness. ∗ Corresponding author: Ramón Quintanilla.
- Exponential stability
- Polynomial stability