Sharp interface limit of the Fisher-KPP equation

We investigate the singular limit, as ε→ 0, of the Fisherequation ∂ₜ u=εΔ u + ε⁻¹u(1-u) in thewhole space. We consider initial data with compact support plus,possibly, perturbations very small as ||x|| → ∞.By proving both generation and motion of interface properties, weshow that the sharp interface limit moves by a constant speed,which is the minimal speed of some related one-dimensionaltravelling waves. Moreover, we obtain a new estimate of thethickness of the transition layers. We also exhibit initial data'not so small' at infinity which do not allow the interfacephenomena.