Electron. J. Diff. Equ., Vol. 2016 (2016), No. 22, pp. 1-14.

Existence and decay of solutions to a viscoelastic plate equation

Salim A. Messaoudi, Soh Edwin Mukiawa

Abstract:
In this article we study the fourth-order viscoelastic plate equation
$$ u_{tt} + \Delta^{2} u -\int_0^t g(t-\tau)\Delta^2u(\tau)d\tau = 0 $$
in the bounded domain $\Omega=(0,\pi)\times(-\ell,\ell)\subset\mathbb{R}^2$ with non traditional boundary conditions. We establish the well-posedness and a decay result.

Submitted October 12, 2015. Published January 13, 2016.
Math Subject Classifications: 35L35, 37B25, 34D20, 74H20, 74H25.
Key Words: Existence; decay; plate viscoelastic; fourth order.

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Salim A. Messaoudi
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Dhahran 31261, Saudi Arabia
email: messaoud@kfupm.edu.sa
  Soh Edwin Mukiawa
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Dhahran 31261, Saudi Arabia
email: g201206120@kfupm.edu.sa

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