On the large time behaviour of the multi-dimensional Fisher-KPP equation with compactly supported initial data

This paper is concerned with the study of the asymptotic behaviour of a multidimensional Fisher-KPP equation posed in an asymptotically homogeneous medium and supplemented together with a compactly supported initial datum. We derive precise estimates for the location of the front before proving the convergence of the solutions towards the travelling front. In particular, we show that the location of the front drastically depends on the rate at which the medium becomes homogeneous at infinity. Fast rate of convergence only changes the location by some constant while lower rate of convergence induces further logarithmic delay.