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July  2019, 18(4): 1637-1662. doi: 10.3934/cpaa.2019078

## New general decay results in a finite-memory bresse system

 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 546, Dhahran 31261, Saudi Arabia

* Corresponding author

Received  April 2018 Revised  July 2018 Published  January 2019

Fund Project: This work is funded by KFUPM under Project IN161006.

This paper is concerned with the following memory-type Bresse system
 $\begin{array}{ll} \rho_1\varphi_{tt}-k_1(\varphi_x+\psi+lw)_x-lk_3(w_x-l\varphi) = 0,\\ \rho_2\psi_{tt}-k_2\psi_{xx}+k_1(\varphi_x+\psi+lw)+ \int_0^tg(t-s)\psi_{xx}(\cdot,s)ds = 0,\\ \rho_1w_{tt}-k_3(w_x-l\varphi)_x+lk_1(\varphi_x+\psi+lw) = 0, \end{array}$
with homogeneous Dirichlet-Neumann-Neumann boundary conditions, where
 $(x,t) \in (0,L) \times (0, \infty)$
,
 $g$
is a positive strictly increasing function satisfying, for some nonnegative functions
 $\xi$
and
 $H$
,
 $g'(t)\leq-\xi(t)H(g(t)),\qquad\forall t\geq0.$
Under appropriate conditions on
 $\xi$
and
 $H$
, we prove, in cases of equal and non-equal speeds of wave propagation, some new decay results that generalize and improve the recent results in the literature.
Citation: Salim A. Messaoudi, Jamilu Hashim Hassan. New general decay results in a finite-memory bresse system. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1637-1662. doi: 10.3934/cpaa.2019078
##### References:

show all references

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