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In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation u l = [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 Fisher-KPP equation. The original problem is transformed into the proper travelling-wave variables, and then a shooting argument is used to show the existence of a saddle-saddle heteroclinic trajectory for a critical value, c* > 0, of the speed c of an autonomous system of ordinary differential equations. Associated with this connection is a sharp-type solution of the nonlinear partial differential equation.

Original publication




Journal article


IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Publication Date





211 - 221