Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 222, pp. 1-7.
Title: Energy decay for degenerate Kirchhoff equations with weakly nonlinear
dissipation
Authors: Mama Abdelli (Univ. Djillali Liabes, Sidi Bel Abbes, Algeria)
Salim A. Messaoudi (King Fahd Univ., Dhahran, Saudi Arabia)
Abstract:
In this article we consider a degenerate Kirchhoff equation wave
equation with a weak frictional damping,
$$
(|u_t|^{l-2}u_t)_t-\Big( \int_{\Omega }|\nabla _x u|^{2}\,dx\Big)^{\gamma }
\Delta _xu+\alpha (t)g(u_t)=0.
$$
We prove general stability estimates using some properties of convex
functions, without imposing any growth condition at the frictional damping
term.
Submitted September 18, 2013. Published October 11, 2013.
Math Subject Classifications: 35B37, 35L55, 74D05, 93D15, 93D20.
Key Words: Decay of solutions; nonlinear; degenerate; Kirchhoff equation.