应兰州大学数学与统计学院邀请，广州大学数学与信息科学学院常清泉博士将于2025年6月18日下午举行线上学术报告。
报告题目: 在扩张区域上耗散偏微分方程解的长时间动力学行为
时 间：6月18日（星期）16：30-17: 30
腾讯会议ID：569-888-541
报告摘要：This presentation investigates the long-term dynamical behavior of dissipative partial differential equations on spatially evolving domains. We propose a novel penalty methodology based on distance function analysis and demonstrate its effectiveness through two paradigmatic cases: the 2D Navier-Stokes equations with moving boundaries and nonlinear damped wave equations in expanding domains.
For the moving boundary Navier-Stokes system, our analysis proceeds through three principal stages: First, we establish global well-posedness and dissipative properties via the penalty approximation scheme. Subsequently, we develop refined regularity estimates through an enhanced penalty formulation. Finally, we demonstrate that the resulting non-autonomous dynamical system admits pullback exponential attractors, confirming its long-term stabilization characteristics.
Regarding the nonlinear damped wave equation in expanding domains, our investigation employs a three-phase approach: The penalty method initially facilitates the proof of local well-posedness for weak solutions. We then rigorously establish energy dissipation mechanisms and asymptotic compactness properties for both penalized and original systems. Ultimately, we prove the existence of pullback attractors for all considered systems, thereby characterizing their global dynamics.
This systematic study not only validates the efficacy of the distance-based penalty method but also provides a unified framework for analyzing evolutionary PDEs on time-dependent domains.
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报告人简介
常清泉博士，现在广州大学数学与信息科学学院从事博士后研究工作，合作导师曹道民研究员。2019年于兰州大学获得理学博士学位，博士生导师孙春友教授。研究方向是无穷维动力系统以及神经网络算法。研究主题包括带有变号阻尼的双曲方程解的长时间行为，带有退化椭圆算子耗散方程的长时间行为，在时间变区域上耗散动力系统的长时间行为以及带有Group Lasso惩罚项神经网络算法的收敛性问题。主持国家自然科学基金青年项目1项，在Izvestiya. Mathematics、Nonlinear Analysis: Real World Applications 、IEEE Transactions on Cybernetics等期刊上发表10篇文章。
数学与统计学院
甘肃应用数学中心
萃英学院
2025年6月17日
