中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人：王 术 教授 (北京工业大学)
题 目：航空发动机中的非线性流固耦合动力学模型
时 间：2020.12.09（星期三）, 14:30-15:30
地 点：腾讯会议，ID：881 256 284
摘 要：本报告介绍航空发动机压气机叶盘叶片振动力学中的一些数学模型，也介绍流固耦合模型在生物医学中的应用。首先基于振动弹性力学中已有的旋转薄壁梁、板或壳的叶片振动非线性动力学模型，结合航空发动机叶盘叶片装置几何结构和跨音速流场中的高转速实际应用特征提出航空发动机叶片振动非线性流固耦合动力学数学模型，并进行数学分析。也介绍医学中血液动力学流固耦合模型。最后介绍我们最近获得的一些不可压流体流固耦合界面运动模型的理论分析结果。
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报告人：陈秀卿 教授 (中山大学)
题 目：Global Existence and Uniqueness analysis of Reaction-Cross-Diffusion Systems
时 间：2020.12.09（星期三）, 15:30-16:30
地 点：腾讯会议，ID：881 256 284
摘 要：The global-in-time existence of weak and renormalized solutions to reaction-cross-diffusion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions are proved. The cross-diffusion part describes the segregation of population species and is a generalization of the Shigesada-Kawasaki-Teramoto model. The diffusion matrix is not diagonal and generally neither symmetric nor positive semi-definite, but the system possesses a formal gradient-flow or entropy structure. The reaction part is of Lotka-Volterra type for weak solutions or includes reversible reactions of mass-action kinetics and does not obey any growth condition for renormalized solutions. Furthermore, we prove the uniqueness of bounded weak solutions to a special class of cross-diffusion systems, and the weak-strong uniqueness of renormalized solutions to the general reaction-cross-diffusion cases.
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报告人：牛冬娟 教授 (首都师范大学)
题 目：Vanishing porosity limit of the coupled Stokes-Brinkman system
时 间：2020.12.09（星期三）, 16:30-17:30
地 点：腾讯会议，ID：881 256 284
摘 要：In this talk, I will discuss with the small porosity asymptotic behavior of the coupled Stokes-Brinkman system in the presence of a curved interface between the Stokes region and the Brinkman region. In particular, we derive a set of approximate solutions, validated via rigorous analysis, to the coupled Stokes-Brinkman system. Of particular interest is that the approximate solution satisfies a generalized Beavers-Joseph-Saffman-Jones interface condition (1.9)with the constant of proportionality independent of the curvature of the interface. It is a joint work with Mingwen Fei and Xiaoming Wang.
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