Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: Decay-error estimates

We consider degenerate Kirchhoff equations with a small parameter in front of the second-order time-derivative. It is well known that these equations admit global soluions when the parameter is small enough, and that these solutions decay with the same rate of solutions of the limit problem (of parabolic type). In this paper we prove decay-error estimates for the difference between a solution of the hyperbolic problem and the solution of the corresponding parabolic problem. Concerning the decay rates, it turns out that the difference decays faster than the two terms separately.