Asymptotic behavior for a nonlinear viscoelastic problem with a velocity-dependent material density.
We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation . We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.
New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.