A Note on the Asymptotic Behavior of Solutions of the KPP Equation

This note is concerned with the convergence (as t → ∞) to travelling waves of solutions u to the initial value problem of the KPP equation \[u_t = uₓₓ + f(u), x ∈ R { and }t > 0.\] A travelling wave φ c is a solution of the form u(x,t) = φ c (x + ct). Estimates for the difference between u and φ c, in a moving coordinate system ξ = x + ct, are given in a weighted supremum norm and in weighted Lᵖ-norm (p 1).