Asymptotic behaviour for the Kirchhoff equation.

In this paper we study the asymptotic behaviour of the solution u of the Kirchhoff equation with small data. More precisely we show that lim(t-->infinity) \\del(k)(u-v)\\(2) + \\del(k)(u-v)(t)\\(2) = 0 for every k is an element of N where v is a suitable solution of an appropriate wave equation. Moreover we give some estimates on lim(t-->infinity)\\del u\\(2).