Convergence of the viscosity solutions in vanishing contact structure problem

Series: 
Dynamical Systems Working Seminar
Friday, January 11, 2019 - 3:00pm
1 hour (actually 50 minutes)
Location: 
Skiles 246
,  
AMSS & GT Math
Organizer: 
In this talk, I will discuss the vanishing contact structure problem, which focuses on the asymptotic behavior of the viscosity solutions uε of Hamilton-Jacobi equation H (x, Du(x), ε u(x)) =c, as the factor ε tends to zero. This is a natural generalization of the vanishing discount problem. I will explain how to characterize the limit solution in terms of Peierls barrier functions and Mather measures from a dynamical viewpoint. This is a joint work with Hitoshi Ishii, Wei Cheng, and Kai Zhao.