Le Huy Chuan; Tsujikawa, Tohru; Yagi, Atsushi Asymptotic behavior of solutions for forest kinematic model. (English) Zbl 1157.35317 Funkc. Ekvacioj, Ser. Int. 49, No. 3, 427-449 (2006). Summary: We continue a study of the mathematical model of a forest ecosystem which has been introduced by Yu. A. Kuznetsov et al. [J. Math. Biol. 32, No. 3, 219–232 (1994; Zbl 0790.92028)]. 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 [Adv. Math. Sci. Appl. 16, No. 2, 393–409 (2006; Zbl 1130.37406)]. 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. Cited in 2 ReviewsCited in 13 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35K57 Reaction-diffusion equations 35B41 Attractors 35K65 Degenerate parabolic equations 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 92D40 Ecology Keywords:Lyapunov function, \(\omega\)-limit set; forestry ecosystem; PDE-ODE system Citations:Zbl 0790.92028; Zbl 1130.37406 PDFBibTeX XMLCite \textit{Le Huy Chuan} et al., Funkc. Ekvacioj, Ser. Int. 49, No. 3, 427--449 (2006; Zbl 1157.35317) Full Text: DOI