【数学与统计及交叉学科前沿论坛------高端学术讲座第167场】

报告题目：Bi-Lipschitz embeddings of attractors defined on multi-dimensional bounded domains

报 告 人：孙春友教授 东华大学

报告时间:2025年10月15日星期三15:00-16:00

报告地点： 腾讯会议 279188663

报告摘要：It is well-known that the finite dimensional reduction can be realized via by constructing bi-Lipschitz Man\'e projections or inertial manifolds for dissipative PDEs, and the known applications were mainly restricted to the PDEs defined on periodic domains with dimension two or three, and usually no longer valid for case such as the space dimensions $d\geq 4$ or general bounded domains. This talk will report our recent attampt in this direction, especially, for some special case, we provide a criterion which can deal with the case of multi-dimensional ($d\geq 4$) general bounded domains (aperiodic). As an application, we prove the existence of bi-Lipschitz Ma\~{n}\'e projections for a class of fractional Cahn-Hillard equations with Kirchhoff-type nonlinearity.             

报告人简介：孙春友，东华大学教授、博士生导师。主要从事无穷维动力系统、非线性分析方面的研究工作。相关工作发表在《 Izv. Math.》、《Math. Ann.》、《Trans. Amer. Math. Soc. 》、《Indiana Univ. Math. J. 》、《SIAM J. Math. Anal.》、《 J. Differential Equations》，《Nonlinearity》等学术期刊上。