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 periodic 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 approaching each other. The main technique here is to characterize the asymptotic behavior of the pulsating traveling front as t → - ∞.