Asymptotic convergence of solutions to the forest kinematic model. (December 2021)

• Record Type: Journal Article
• Authors: Iwasaki, Satoru
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Forest kinetic model -- Lyapunov function -- Łojasiewicz–Simon gradient inequality -- Asymptotic convergence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103382
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the asymptotic behavior of global solutions to forest kinetic model equations composed of young trees, old trees, and air-borne seeds. Under some parameter assumptions, we prove the asymptotic convergence of global solutions to a stationary solution. To this end, we show a non-smooth version of the Łojasiewicz–Simon gradient inequality on a suitable functional space and a certain norm estimate of the time derivative of global solutions.