具有变系数旋转惯性的含变系数Kirchhoff型方程的长时间动力学
Long-Time Dynamics of Variable-Coefficient Kirchhoff-Type Equations with Variable Rotational Inertia
DOI: 10.12677/AAM.2025.147354, PDF,   
作者: 卢京鑫：丽江文化旅游学院，云南 丽江；吕鹏辉*：苏州大学应用技术学院，江苏 苏州
关键词: 变系数型Kirchhoff方程；变系数旋转惯性；整体吸引子；Kirchhoff-Type Equation with Variable Coefficients； Variable-Coefficient Rotational Inertia； Global Attractor
摘要: 本文研究了具变系数旋转惯性的含变系数Kirchhoff型方程的渐近行为的问题，在合理的假设条件 下，利用先验估计、 菜布尼兹公式及经典Galerkin方法，获得了方程整体解的存在唯一性和该类 方程的整体吸引子这一结果，推广了Kirchhoff方程关于整体吸引子的结果。
Abstract: This paper investigates the asymptotic behavior of a variable-coefficient Kirchhoff-type equation with rotational inertia. Under suitable assumptions, we establish the exis- tence and uniqueness of global solutions and prove the existence of a global attractor for the equation by employing a priori estimates, the Leibniz formula, and the classi- cal Galerkin method. These results extend the existing theory of global attractors for Kirchhoff-type equations.
文章引用：卢京鑫, 吕鹏辉. 具有变系数旋转惯性的含变系数Kirchhoff型方程的长时间动力学[J]. 应用数学进展, 2025, 14(7): 158-173. https://doi.org/10.12677/AAM.2025.147354

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