Journal of Prime Research in Mathematics

Vol. 19 (2023), Issue 2, pp. 116 – 134
ISSN: 1817-3462E (Online) 1818-5495 (Print)

Well-posedness and exponential stability for a piezoelectric beams system with magnetic and thermal effects in the presence of past history

Hassan Messaoudi\(^a\), Houssem Eddine Khochemane\(^b\), Abdelouaheb Ardjouni\(^{c,∗}\), Salah Zitouni\(^a\),

\(^a\)Laboratory of Informatics and Mathematics, Department of Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras,41000, Algeria.

\(^b\)Ecole normale sup´erieure d’enseignement technologique, Azzaba, Skikda, 21000, Algeria.

\(^c\)Department of Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria.

Correspondence should be addressed to: hassanmessaoudi1997@gmail.com, khochmanehoussem@hotmail.com, abd_ardjouni@yahoo.fr, zitsala@yahoo.fr

Copyright © 2024 Hassan Messaoudi, Houssem Eddine Khochemane, Abdelouaheb Ardjouni, Salah Zitouni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 4 November 2022 Accepted: 20 January 2024; Published Online: 22 January 2024.

Abstract

In this article, we consider the one-dimensional system of piezoelectric beams with thermal and magnetic effects in the presence of an infinite memory term acting on the mechanical equation. Under appropriate assumptions on the kernel, we prove that the system is well-posed in the sense of semigroup and by constructing a suitable Lyapunov functional. We establish that the system is exponentially stable. Moreover,our result does not depend on any relationship between system parameters.

Keywords:

Piezoelectric beams, past history, semigroup approach, Lyapunov functional, energy method, exponential stability.