We consider Kirchhoff equations with a small parameter epsilon in front of the second-order time-derivative, and a dissipative term whose coefficient may tend to 0 as t -> + infinity (weak dissipation). In this note we present some recent results concerning existence of global solutions, and their asymptotic behavior both as t -> + infinity and as epsilon -> 0. Since the limit equation is of parabolic type, this is usually referred to as a hyperbolic-parabolic singular perturbation problem. We show in particular that the equation exhibits hyperbolic or parabolic behavior depending on the values of the parameters.
|Autori:||GHISI M; GOBBINO M|
|Titolo:||Hyperbolic-parabolic singular perturbation for Kirchhoff equations with weak dissipation|
|Anno del prodotto:||2010|
|Appare nelle tipologie:||1.1 Articolo in rivista|