2 research outputs found
Sharp large time behaviour in n-dimensional Fisher-KPP equations
We study the large time behaviour of the Fisher-KPP equation âtu = âu+uâu2 in spatial dimension N, when the initial datum is compactly supported. We prove the existence of a Lipschitz function sâ of the unit sphere, such that u(t, x) approaches, as t goes to infinity, the function Ucâ ( |x| â cât + Nc+â2 lnt + sâ(|xx| )) , where Ucâ is the 1D travelling front with minimal speed câ = 2. This extends an earlier result of GĂ€rtner