Entire solutions of the Fisher-KPP equation in time periodic media

Abstract

This paper is concerned with the existence of the pulsating type entire solutions of the Fisher-KPP equation with advection term in time peri- odic media. By constructing appropriate subsolutions and supersolutions, we prove that there exists a pulsating type entire solution which behaves as two pulsating traveling fronts coming from two opposite directions and approach- ing each other. The main technique here is to characterize the asymptotic behavior of the pulsating traveling front as t ! 1 .