A SHOOTING ARGUMENT APPROACH TO A SHARP-TYPE SOLUTION FOR NONLINEAR DEGENERATE FISHER-KPP EQUATIONS

In this paper we prove the existence and uniqueness of a travelling-wa ve solution of sharp type for the degenerate (at u=0) parabolic equati on u,=[D(u)u(x)](x)+g(u) where D is a strictly increasing function and g is a function which generalizes the kinetic part of the classical F isher-KPP equation. The original problem is transformed into the prope r travelling-wave variables, and then a shooting argument is used to s how the existence of a saddle-saddle heteroclinic trajectory for a cri tical value, c>0, of the speed c of an autonomous system of ordinary differential equations. Associated with this connection is a sharp-typ e solution of the nonlinear partial differential equation.