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arXiv · 2308.04231

Stabilization of piezoelectric beam with Coleman-Gurtin or Gurtin-Pipkin thermal law and under Lorenz gauge condition

Dounya Kechiche·Ammar Khemmoudj
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Abstract

In this paper, we present the analysis of stability for a piezoelectric beam subject to a thermal law (Coleman-Gurtin or Gurtin-Pipkin thermal law) adding some viscous damping mechanism to the electric field in $x-$direction and $z-$direction, and we discuss several cases. Then, there is no need to control the electrical field components in $x$-direction and $z-$ direction to establish an exponential decay of solutions when the beam is subjected to a Coleman-Gurtin law, otherwise a polynomial stability is established with Gurtin-Pipkin thermal law in case when the electrical field components are damped.

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Dounya Kechiche, Ammar Khemmoudj. 2023-08-08. Stabilization of piezoelectric beam with Coleman-Gurtin or Gurtin-Pipkin thermal law and under Lorenz gauge condition. https://arxiv.org/abs/2308.04231

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