10月15日 中国科学院李天虹副研究员学术报告

发布时间:2019-10-13   浏览次数:10

报 告 人: 李天虹 副研究员(中国科学院数学与系统科学研究院)

报告题目:Singular set of viscosity solutions to Eikonal equation

报告时间:2019年10月15日(周二)上午10:30

报告地点:静远楼204学术报告厅

报告人简介:

李天虹,美国西北大学博士,现任中国科学院数学与系统科学研究院副研究员。主要成果包括:补偿列紧方法证明L^无穷意义下熵解的存在性;弱解的L^1稳定性和唯一性;可压欧拉方程组的特解;半鞅从微分流形到标架丛的水平提升系等,在《Arch. Ration. Mech. Anal.》《Z. Angew.Math. Phys.》、《J. Differential Equations》等世界著名杂志上发表论文十多篇,并被广泛引用。

报告摘要:

The evolutionary Eikonal equation is a Hamilton-Jacobi equation with Hamiltonian $H(P)=|P|$, which is not strictly convex nor smooth. The regularizing effect of Hamiltonian for the Eikonal equation is much weaker than that of strictly convex Hamiltonians, therefore leading to new phenomena. In this talk, we discuss the set of singularity points of solutions in the upper half space for $C^1$ or $C^2$ initial data, with emphasis on the countability of connected components of the set.

The regularity of solutions in the complement of the set of singularity points is also obtained.