Abstract:
Homogenization of Hamilton-Jacobi (inviscid) equations and Hamilton-Jacobi-Bellman (viscous) equations in periodic and in stationary ergodic media has received a lot of attention since the pioneer work of Lions, Papanicolaou and Varadhan. These problems arise naturally in applications such as optimal control and combustion in heterogeneous environments. In this talk I will review some key results for the stochastic homogenization of HJB equation, and discuss some recent progress we have on the stochastic homogenization of HJ equation with a vanishing non-local term modeling jump-diffusion. Our approach is by an adaption of the method developed by Kosygina, Rezakhanlou and Varadhan (CPAM 2006). This work is joint with Dr. Qi Zhang from BIMSA.
Biography:
Dr. Jing Wenjia is an Associate Professor at Yau Mathematical Sciences Center, Tsinghua University. Prior to joining Tsinghua University, Professor Jing has held various positions, including L.E. Dickson Instructor at the University of Chicago and Postdoctoral Researcher at Ecole Normale Supérieure. He obtained his Ph.D. in Applied Mathematics from Columbia University in 2011, under the supervision of Guillaume Bal, following a B.S. in Theoretical and Applied Mechanics from Peking University. Professor Jing's research focuses on Analysis and Partial Differential Equations, Stochastic Homogenization and Quantitative Estimates, Waves Propagation in Random Media, and other Applied Analysis.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.