Spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media

Abstract

The current paper is devoted to the study of spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media. We first prove the existence, uniqueness, and stability of spatially homogeneous entire positive solutions. Next, we establish lower and upper bounds of the (generalized) spreading speed intervals. Then, by constructing appropriate sub-solutions and super-solutions, we show the existence and continuity of transition fronts with given front position functions. Also, we prove the existence of some kind of critical front.