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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 2, 2020, pp. 185–222
DOI: 10.4171/ZAA/1657

Published online: 2020-04-07

Existence and New General Decay Results for a Viscoelastic Timoshenko System

Jamilu Hashim Hassan[1], Salim A. Messaoudi[2] and Mostafa Zahri[3]

(1) King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
(2) University of Sharjah, United Arab Emirates
(3) University of Sharjah, United Arab Emirates

In this paper, we are concerned with a memory-type Timoshenko system with Dirichlet boundary conditions and a very general class of relaxation functions. We prove the existence and uniqueness of solutions of the system as well as some new decay results which generalize and improve many earlier ones in the literature. We consider the case of equal-speeds and the case of non-equal-speeds of propagation. We also give some numerical illustrations and related comparisons.

Keywords: Timoshenko system, viscoelastic, general and optimal decay, equal and non-equal speeds of wave propagation

Hassan Jamilu Hashim, Messaoudi Salim, Zahri Mostafa: Existence and New General Decay Results for a Viscoelastic Timoshenko System. Z. Anal. Anwend. 39 (2020), 185-222. doi: 10.4171/ZAA/1657