Research article

Uniqueness and exponential instability in a new two-temperature thermoelastic theory

  • Received: 28 January 2021 Accepted: 11 March 2021 Published: 15 March 2021
  • MSC : 35Q74, 74H10, 74H25, 80A19, 74F05

  • In this work we consider the temperature-rate dependent two temperatures thermoelastic theory. It has been proposed very recently. We study the case in which the elasticity tensor may not be positive definite. Thus, the problem can be ill posed in the sense of Hadamard. We adapt the logarithmic convexity argument to the specific situation proposed by this theory. That is, we define a suitable function on the solutions satisfying that the logarithm is convex. Uniqueness and instability of the solutions under suitable conditions on the constitutive tensors are proved.

    Citation: José R. Fernández, Ramón Quintanilla. Uniqueness and exponential instability in a new two-temperature thermoelastic theory[J]. AIMS Mathematics, 2021, 6(6): 5440-5451. doi: 10.3934/math.2021321

    Related Papers:

  • In this work we consider the temperature-rate dependent two temperatures thermoelastic theory. It has been proposed very recently. We study the case in which the elasticity tensor may not be positive definite. Thus, the problem can be ill posed in the sense of Hadamard. We adapt the logarithmic convexity argument to the specific situation proposed by this theory. That is, we define a suitable function on the solutions satisfying that the logarithm is convex. Uniqueness and instability of the solutions under suitable conditions on the constitutive tensors are proved.



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