中科院数学与系统科学研究院

数学研究所

学术报告

动力系统研讨班

报告人：程伟（南京大学）

题  目：Singularities propagation in deterministic and random setting

时  间：2023.12.06（星期三）10:00-11:00

地  点：数学院南楼N913

摘  要：There are various notions of singular characteristics in the theory of propagation singularities of viscosity solutions. In this talk, we will discuss the variational construction of generalized characteristics  and strict singular characteristics. We proved the solution of generalized characteristics can be constructed in an intrinsic way using the idea of minimizing movements and certain process of homogenization.  Moreover, the relation between the strict singular characteristics and the EDI-EVI frame of gradient flow was also discussed. In general, these results bridge various different topics. We also discuss a random setting of this story which is closely connnected to optimal mass transport. This talk is based on our latest work with Piermarco Cannarsa, Jiahui Hong, Kaizhi Wang and Tianqi Shi.