Well-posedness and polynomial energy decay rate of a transmission problem for Rayleigh beam model with heat conduction

Article type: Research Article

Authors: Akil, Mohammad^a | Ghader, Mouhammad^{b; *} | Hajjej, Zayd^c | Sammoury, Mohamad Ali^b

Affiliations: [a] INSA Hauts-de-France, CERAMATHS-Laboratoire de Matériaux Céramiques et de Mathématiques, Univ. Polytechnique Hauts-de-France, F-59313 Valenciennes, France | [b] Department of Mathematics, Al Maaref University, Beirut Campus, Airport Bridge, Ghobeiry 5078 0025, Lebanon | [c] Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, we investigate the stability of the transmission problem for Rayleigh beam model with heat conduction. First, we reformulate our system into an evolution equation and prove our problem’s well-posedness. Next, we demonstrate the resolvent of the operator is compact in the energy space, then by using the general criteria of Arendt–Batty, we prove that the thermal dissipation is enough to stabilize our model. Finally, a polynomial energy decay rate has been obtained which depends on the mass densities and the moments of inertia of the Rayleigh beams.

Keywords: Rayleigh beam, heat conduction, C₀-semigroup, polynomial stability

DOI: 10.3233/ASY-231849

Journal: Asymptotic Analysis, vol. 135, no. 1-2, pp. 115-156, 2023