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<p>In this work, we will study, from the analytical point of view, two problems arising in second-gradient thermoelasticity. The first one involves the Lord–Shulman second-gradient theory. An existence and uniqueness result is shown by using the theory of linear semigroups. Then, we prove that the energy decay is of exponential type and that the semigroup associated to the differential operator is not differentiable, which implies that this is not analytic neither. The second problem includes the so-called Moore–Gibson–Thompson second-gradient theory. Two cases will be considered if we assume that the thermal law includes (or not) fourth-order spatial derivatives. In the case of second-order spatial derivatives, we recall that the problem has a unique solution but the energy decay is slow; meanwhile, if fourth-order spatial derivatives are present, the decay is of exponential type. For this last problem, we study the analyticity of the semigroups depending on a constitutive coefficient.</p>

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Decay and regularity in second-gradient thermoelastic plates with relaxation time

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月8日

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  • José R. Fernández,
  • Ramón Quintanilla

摘要

In this work, we will study, from the analytical point of view, two problems arising in second-gradient thermoelasticity. The first one involves the Lord–Shulman second-gradient theory. An existence and uniqueness result is shown by using the theory of linear semigroups. Then, we prove that the energy decay is of exponential type and that the semigroup associated to the differential operator is not differentiable, which implies that this is not analytic neither. The second problem includes the so-called Moore–Gibson–Thompson second-gradient theory. Two cases will be considered if we assume that the thermal law includes (or not) fourth-order spatial derivatives. In the case of second-order spatial derivatives, we recall that the problem has a unique solution but the energy decay is slow; meanwhile, if fourth-order spatial derivatives are present, the decay is of exponential type. For this last problem, we study the analyticity of the semigroups depending on a constitutive coefficient.