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

Authors

  • Hassan Messaoudi Laboratory of Informatics and Mathematics, Department of Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria.
  • Houssem Eddine Khochemane Ecole normale sup´erieure d’enseignement technologique, Azzaba, Skikda, 21000, Algeria.
  • Abdelouaheb Ardjouni Department of Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria.
  • Salah Zitouni Laboratory of Informatics and Mathematics, Department of Mathematics, University of Souk-Ahras, P.O. Box 1553, Souk-Ahras, 41000, Algeria.

Keywords:

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

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.

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Published

2023-12-31

Issue

Vol. 19 No. 2 (2023): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

Well-posedness and exponential stability for a piezoelectric beams system with magnetic and thermal effects in the presence of past history. (2023). Journal of Prime Research in Mathematics, 19(2), 116–134. https://jprm.sms.edu.pk/index.php/jprm/article/view/219