×

Asymptotic behavior of solutions for forest kinematic model. (English) Zbl 1157.35317

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.

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
PDFBibTeX XMLCite
Full Text: DOI