RESEARCH ARTICLE

Exponential and polynomial decay for a laminated beam with Fourier's law of heat conduction and possible absence of structural damping

  • Wenjun LIU ,
  • Weifan ZHAO
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  • School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received date: 28 Feb 2020

Accepted date: 19 Jul 2021

Copyright

2021 Higher Education Press

Abstract

We study the well-posedness and decay properties of a onedimensional thermoelastic laminated beam system either with or without structural damping, of which the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is wellposed by using the Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method. When the speeds are not equal, whether the system without structural damping may has polynomial stability is left as an open problem.

Cite this article

Wenjun LIU , Weifan ZHAO . Exponential and polynomial decay for a laminated beam with Fourier's law of heat conduction and possible absence of structural damping[J]. Frontiers of Mathematics in China, 2021 , 16(4) : 997 -1021 . DOI: 10.1007/s11464-021-0964-z

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