Asymptotic convergence of solutions to the forest kinematic model

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 Lojasiewicz-Simon gradient inequality on a suitable functional space and a certain norm estimate of the time derivative of global solutions. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

In this study, we analyze the asymptotic behavior of global solutions to forest kinetic model equations consisting of young trees, old trees, and air-borne seeds. We prove the asymptotic convergence of global solutions to a stationary solution under certain parameter assumptions by demonstrating a non-smooth version of the Lojasiewicz-Simon gradient inequality and a norm estimate of the time derivative of global solutions on a suitable functional space.