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.

中文翻译：

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森林运动学模型解的渐近收敛

我们研究了由幼树、老树和空气传播的种子组成的森林动力学模型方程的全局解的渐近行为。在一些参数假设下，我们证明了全局解对平稳解的渐近收敛。为此，我们在合适的函数空间上展示了 Łojasiewicz-Simon 梯度不等式的非平滑版本和全局解的时间导数的某个范数估计。