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

2023/08/08 by Kechiche, Dounya, Khemmoudj, Ammar
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.04231

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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