  In this paper, we consider energy decay estimates for the following nonlinear
evolution problem $$\begin{split} [P(u_t(t))]_t + A u(t) + B(t , x , u_t(t))
=0,\quad t\in J=(0,\infty), \end{split}$$ under suitable assumptions on the
self-adjoint operators $P$ and $B$ and the divergence operator $A$. The work
extends the earlier work of Marcati, Nakao, Levin and Pucci on abstract
evolution equations to the case with possibly nonlinear damping. The technique
also differs from earlier techniques. Here, we make use of a modified perturbed
energy technique.
