Sharp asymptotics for the multidimensional KPP equation

In this article sharp asymptotics for the solution of nonhomogeneous Kolmog orov, Petrovskii and Pisciunov equation depending on a small parameter are considered when the initial condition is the characteristic function of a s et A is an element of R-d. We show how to extend the Ben Arous and Rouault' s result that dealt with d = 1 and the initial condition as the characteris tic function of A = (x less than or equal to 0). The dependance of the asym ptotics on the geometry of the boundary of A is precisely described for the problem with constraints. (C) 1999 Elsevier Science B.V. All rights reserv ed.