Asymptotic Behavior of Solutions for Forest Kinematic Model

MR2297947 Chuan, Le Huy, Tsujikawa, Tohru and Yagi, Atsushi Le Huy CHUAN, Tohru TSUJIKAWA and Atsushi YAGI Asymptotic Behavior of Solutions for Forest Kinematic Model Funkcialaj Ekvacioj. Serio Internacia 49 2006 427--449 http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-3/49_427.pdf http://www.ams.org/mathscinet-getitem?mr=MR2297947 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 $\omega$-limit sets, namely, $\omega(U_0)\subset L^2-\omega(U_0)\subset w^*-\omega(U_0)$, for each point $U_0$ of the dynamical system which was constructed in our preceding paper [1]. Using a Lyapunov function, we will then investigate basic properties of these $\omega$-limit sets. Especially it shall be shown that $L^2$-$\omega(U_0)$ consists of stationary solutions alone. Asymptotic behavior of solutions, Dynamical system, Lyapunov function, $\omega$-limit set, Forestry ecosystem. 39A11, 34K14. 49-427 2006 Asymptotic Behavior of Solutions for Forest Kinematic Model CHUAN, Le Huy, TSUJIKAWA, Tohru and YAGI, Atsushi Le Huy CHUAN, Tohru TSUJIKAWA and Atsushi YAGI 1 Chuan, L. H.; Yagi, A., Dynamical system for forest kinematic model, Adv. Math. Sci. Appl., 16 (2006), to appear 2 Chuan, L. H.; Tsujikawa, T.; Yagi, A., Structure of stationary solutions for forest kinematic model, submitted

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