Speaker: Dr. Qinbo Chen (MCM)

Title: Convergence of viscosity solutions in the vanishing contact structure problem

Time: 15:30-16:30, Nov 29, 2018

Place: N817

Abstract: I will present a joint work with Hitoshi Ishii, Wei Cheng and Kai Zhao on 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 goes to zero. It is a natural generalization of the vanishing discount problem which was first studied in a general framework by P.-L. Lions, G. Papanicolaou and S. Varadhan. In this talk, I will first briefly introduce some basic notations and results in Aubry-Mather theory and weak KAM theory. Then I will explain how to characterize the limit solution in terms of Peierls barrier functions and Mather measures from a dynamical viewpoint.