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2018 General and optimal decay in a memory-type Timoshenko system
Salim A. Messaoudi, Jamilu Hashim Hassan
J. Integral Equations Applications 30(1): 117-145 (2018). DOI: 10.1216/JIE-2018-30-1-117


This paper is concerned with the following memory-type Timoshenko system \[ \rho _1\varphi _{tt}-K(\varphi _x+\psi )_x=0 \] \[ \rho _2\psi _{tt}-b\psi _{xx}+K(\varphi _x+\psi )+ \displaystyle \int _0^tg(t-s)\psi _{xx}(s)\,ds=0, \] $(x,t)\in (0,L)\times (0,\infty )$, with Dirichlet boundary conditions, where $g$ is a positive non-increasing function satisfying, for some constant $1\leq p\lt {3}/{2}$, \[ g'(t)\leq -\xi (t)g^p(t),\quad \mbox {for all }t\geq 0. \] We prove some decay results which generalize and improve many earlier results in the literature. In particular, our result gives the optimal decay for the case of polynomial stability.


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Salim A. Messaoudi. Jamilu Hashim Hassan. "General and optimal decay in a memory-type Timoshenko system." J. Integral Equations Applications 30 (1) 117 - 145, 2018.


Published: 2018
First available in Project Euclid: 10 April 2018

zbMATH: 06873401
MathSciNet: MR3784885
Digital Object Identifier: 10.1216/JIE-2018-30-1-117

Primary: 35B05 , 35L05 , 35L15 , 35L70

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

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.30 • No. 1 • 2018
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