Energy decay of solutions for the wave equation with a time varying delay term in the weakly nonlinear internal feedbacks

Mohamed Ferhat

doi:10.26637/mjm402/013

Abstract

We consider the nonlinear wave equation in a bounded domain with a time varying delay term in the weakly nonlinear internal feedback
\begin{align*}
&\left(\left|u_t\right|^{\gamma-2} u_t\right)_t-\Delta_x u-\int_0^t g(t-s) \Delta u(s) d s\\&+\mu_1 \psi\left(u_t(x, t)\right)+\mu_2 \psi\left(u_t(x, t-\tau(t))\right)=0,
\end{align*}
we study the asymptotic behavior of solutions in using the Lyapunov functional, we extend and improve the previous result due to [30].

Keywords:

Energy decay, viscoelastic term, time varying delay term

Mathematics Subject Classification:

34G20

Authors Imprint References Funding Related Articles Downloads

Mohamed Ferhat Department of Mathematics, Usto University – P. O. Box 89, Oran 31000, ALGERIA.

Pages: 284-296
Date Published: 01-04-2016
Vol. 4 No. 02 (2016): Malaya Journal of Matematik (MJM)

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