动态边界条件下退化抛物方程的指数吸引子

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (4): 157-165.

动态边界条件下退化抛物方程的指数吸引子

李心, 刘孔玉, 刘洋^*

燕山大学理学院, 河北秦皇岛 066004

收稿日期:2023-05-25 出版日期:2025-08-28 发布日期:2025-09-05
通讯作者: 刘洋(1992-),男,河南信阳人,讲师.Email:lliuyang@ysu.edu.cn
基金资助:
国家自然科学基金(11801493),河北省教育厅高等学校科技计划青年基金(QN2020203),河北省自然科学基金(A2022203004)

Exponential attractor for degenerate parabolic equations with dynamic boundary conditions

LI Xin, LIU Kong-yu, LIU Yang

School of Science, Yanshan University, Qinhuangdao 066004, China

Received:2023-05-25 Online:2025-08-28 Published:2025-09-05

摘要/Abstract

摘要： 与经典的边界条件不同,动态边界条件由于其特有的耦合性使得系统长时间性态的研究具有本质性的困难.针对具有动态边界条件的非自治退化抛物方程,研究了其在有界区域上拉回指数吸引子的存在性.通过能量方法建立解过程在吸收集内的Lipschitz连续性;利用正交投影分解解过程,并证明非正交部分的解过程在吸收集内的压缩性;根据Banach空间中拉回指数吸引子的存在性定理得到该方程指数吸引子的存在性.

关键词: 动态边界条件, 退化抛物方程, 拉回指数吸引子, 非自治

Abstract: Different from the classical boundary conditions, the dynamic boundary conditions present fundamental challenges in studying the long-time behavior of the system because of their unique coupling. For the non-autonomous degenerate parabolic equations with dynamic boundary conditions, the existence of the pullback exponential attractor in a bounded domain was studied. The Lipschitz continuity of the solution process within the absorbing sets was established using the energy method. The solution process was decomposed by orthogonal projection, and the compressibility of the solution process of the non-orthogonal parts within the absorbing sets was proved. According to the existence theorem of the pullback exponential attractor in Banach space, the existence of the exponential attractor of the equation was obtained.

Key words: dynamic boundary conditions, degenerate parabolic equation, pullback exponential attractors, non-autonomous

中图分类号:

O175.2

李心, 刘孔玉, 刘洋. 动态边界条件下退化抛物方程的指数吸引子[J]. 兰州理工大学学报, 2025, 51(4): 157-165.

LI Xin, LIU Kong-yu, LIU Yang. Exponential attractor for degenerate parabolic equations with dynamic boundary conditions[J]. Journal of Lanzhou University of Technology, 2025, 51(4): 157-165.

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