Stochastic homogenization of Hamilton-Jacobi equations: an overview of results and challenges

Applied analysis seminar

Organizer：

Wenjia Jing 荆文甲（YMSC）

Speaker：

Elena Kosygina

(NYU Shanghai & CUNY）

Time：

Fri., 16:00-17:00, Nov. 29, 2024

Venue：

B548, Shuangqing Complex Building A

Title：

Stochastic homogenization of Hamilton-Jacobi equations: an overview of results and challenges

Abstract：

Since the pioneering unpublished paper of P.-L. Lions, G. Papanicolaou, S.R.S. Varadhan (circa 1987), where they proposed two different approaches to the homogenization problem for Hamilton-Jacobi equations with periodic Hamitonians, the subject of homogenization of inviscid and viscous Hamilton-Jacobi equations in stationary ergodic media has received a lot of attention. In this talk I shall first give a very brief overview of the topic and then focus on our latest results and open questions. These latest results are the joint work with Atilla Yilmaz from Temple University.