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

TL;DR

This paper investigates the spreading speeds and transition fronts of lattice KPP equations in media with time heterogeneity, establishing key properties and bounds for solutions and fronts.

Contribution

It introduces new results on the existence, uniqueness, and stability of solutions and transition fronts in time-heterogeneous lattice KPP equations.

Findings

Proved existence and stability of positive solutions

Established bounds for spreading speed intervals

Constructed transition fronts with specified positions

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.