Asymptotic Behavior of Solutions for Forest Kinematic Model

Abstract

We continue a study of the mathematical model of forest ecosystem which has been introduced by Kuznetsov et al. [3]. In this paper, we will introduce three kinds of ω-limit sets, namely, ω(U₀) ⊂ L²-ω(U₀) ⊂ w^*-ω(U₀), for each point U₀ of the dynamical system which was constructed in our preceding paper [1]. Using a Lyapunov function, we will then investigate basic properties of these ω-limit sets. Especially it shall be shown that L²-ω(U₀) consists of stationary solutions alone.