| Abstract: |
| In 1987, Lions firstly proposed the homogenization for Hamilton-Jacobi equations, which revealed the significance of effective Hamiltonian in controlling the large time behavior of solutions. He also pointed out a vanishing discount procedure which is equivalent in obtaining the effective Hamiltonian, yet the convergence of solutions in this procedure was unknown until recently. In a bunch of joint works, we verified this convergence by using dynamical techniques. |
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