Speaker: 金亮 (南京理工大学)
Time: 2025-12-11 16:30-17:30
Location: 1310, SIMIS
摘要：
In this talk, we first review some results and terminologies in the weak KAM theory for contact Hamilton-Jacobi equations, then focus on some recent progress concerning the inhomogeneous discounted Hamilton-Jacobi equation λ(x)u + h(x, dₓu) = c. Our discussion will cover: (1) the definition of the critical value and the solvability of the ergodic problem; (2) the relationship between the critical value and the existence of locally asymptotically stable solutions; (3) the distribution of Mather measures; (4) the long-time behavior and convergence rate of the solution semigroup; (5) the impact of the energy parameter c on the convergence rate of the solution semigroup, and the limiting state as c tends to infinity. If time permits, we will also report some results for the critical case and some problems for future study.
About Speaker:
Jin Liang is an Associate Professor at the School of Mathematics and Statistics, Nanjing University of Science and Technology. His research areas include Hamiltonian dynamical systems, with current interests in dynamics of contact Hamiltonian systems and Hamilton–Jacobi equations, Lorentz geometry and causality theory, and symplectic/contact geometry. His ongoing projects focus on variational principles for contact Hamiltonian systems and the variational construction of asymptotic orbits; attractors of monotone systems; the structure of viscosity solutions and dynamics of the solution semigroup for non-monotone contact Hamilton–Jacobi equations; representations of viscosity solutions for weakly coupled Hamilton–Jacobi systems and the vanishing discount problem; and weak KAM theory for Lorentz geodesic flows and the Borde–Sorkin conjecture. He has published in journals such as JMPA, CVPDE, Nonlinearity, JDE, and Geom. Dedicata.
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