In this paper we consider the following three-phase-lag thermoelastic plate: (Formula presented.) We obtain analyticity and exponential stability for the associated (Formula presented.) -semigroup when the coefficients satisfy (Formula presented.). The analyticity of the semigroup still holds when (Formula presented.). However, the instability of solution was proved by the Routh–Hurwitz rule.
Bibliographical noteFunding Information:
The work of R. Quintanilla was supported by projects ‘Análisis Matemáticode Problemas de la Termomecánica’ (MTM2016-74934-P) (AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness, and ‘Análisis Matemático Aplicado a la Termomecánica’ (Ref. PID2019- 105118GB-I00), (AEI/FEDER, UE) of the Spanish Ministry of Science, Innovation and Universities.
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- exponential stability
- Three-phase-lag thermoelastic plate