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Lack of exponential decay for a laminated beam with structural damping and second sound

Volume 124 / 2020

Wenjun Liu, Xiangyu Kong, Gang Li Annales Polonici Mathematici 124 (2020), 281-289 MSC: Primary 35L05; Secondary 93C20, 93D20, 34B05. DOI: 10.4064/ap181224-17-9 Published online: 6 February 2020

Abstract

In [Z. Angew. Math. Phys. 68 (2017)] Apalara considered a one-dimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depending on the stability number $\chi _\tau $. In this short note, we continue the study of the same system and show that the solution lacks exponential decay if $\chi _\tau \neq 0$, which solves an open problem proposed by Apalara.

Authors

  • Wenjun LiuNanjing University of Information Science and Technology
    School of Mathematics and Statistics
    210044, Nanjing, China
    e-mail
  • Xiangyu KongNanjing University of Information Science and Technology
    School of Mathematics and Statistics
    210044, Nanjing, China
    e-mail
  • Gang LiNanjing University of Information Science and Technology
    School of Mathematics and Statistics
    210044, Nanjing, China
    e-mail

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