Transition fronts of KPP-type lattice random equations

TL;DR

This paper studies the existence and stability of wave solutions called transition fronts in KPP-type lattice equations within random media, revealing how randomness influences wave behavior.

Contribution

It establishes comparison principles, constructs transition fronts, and proves their stability in stochastic lattice equations, advancing understanding of wave dynamics in random environments.

Findings

Existence of random transition fronts proved

Stability of these fronts demonstrated

Media and randomness influence wave profiles and speeds

Abstract

In this paper, we investigate the existence and stability of random transition fronts of KPP-type lattice equations in random media, and explore the influence of the media and randomness on the wave profiles and wave speeds of such solutions. We first establish comparison principle for sub-solutions and super-solutions of KPP type lattice random equations and prove the stability of positive constant equilibrium solution. Next, by constructing appropriate sub-solutions and super-solutions, we show the existence of random transition fronts. Finally, we prove the stability of random transition fronts of KPP-type lattice random equations.