On uniqueness and instability for some thermomechanical problems involving the Moore– Gibson–Thompson equation
MOORE-GIBSON-THOMPSON EQUATION.pdf (394,9Kb) (Restricted access) Request copy
Què és aquest botó?
Aquest botó permet demanar una còpia d'un document restringit a l'autor. Es mostra quan:
- Disposem del correu electrònic de l'autor
- El document té una mida inferior a 20 Mb
- Es tracta d'un document d'accés restringit per decisió de l'autor o d'un document d'accés restringit per política de l'editorial
Rights accessRestricted access - publisher's policy (embargoed until 2021-05-09)
It is known that in the case that several constitutive tensors fail to be positive definite the system of the ther- moelasticity could become unstable and, in certain cases, ill-posed in the sense of Hadamard. In this paper, we consider the Moore–Gibson–Thompson thermoelasticity in the case that some of the constitutive tensors fail to be positive and we will prove basic results concerning uniqueness and instability of solutions. We first consider the case of the heat conduction when dissipation condition holds, but some constitutive tensors can fail to be positive. In this case, we prove the uniqueness and instability by means of the logarithmic convexity argument. Second we study the thermoelastic system only assuming that the thermal conductivity tensor and the mass density are positive and we obtain the uniqueness of solutions by means of the Lagrange identities method. By the logarithmic convexity argument we prove later the instability of solutions whenever the elasticity tensor fails to be positive, but assuming that the conductivity rate is positive and the thermal dissipation condition hold. We also sketch similar results when conductivity rate and/or the thermal conductivity fail to be positive definite, but the elasticity tensor is positive definite and the dissipation condition holds. Last sections are devoted to considering the case when a third-order equation is proposed for the displacement (which comes from the viscoelasticiy). A similar study is sketched in these cases.
CitationPellicer, M.; Quintanilla, R. On uniqueness and instability for some thermomechanical problems involving the Moore– Gibson–Thompson equation. "Zeitschrift für angewandte Mathematik und Physik", Juny 2020, vol. 71, núm. 3, p. 81-1-81-21.
|MOORE-GIBSON-THOMPSON EQUATION.pdf||394,9Kb||Restricted access|