Title: Asymptotic analysis for Hamilton-Jacobi equations with large drift term,
Abstract: We investigate the asymptotic behavior of solutions of Hamilton-Jacobi
equations with large drift term in an open subset of two-dimensional Euclidean
space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a
Hamiltonian $H$, with $\varepsilon > 0$, we establish the convergence, as
$\varepsilon \to 0+$, of solutions of the Hamilton-Jacobi equations and
identify the limit of the solutions as the solution of systems of ordinary
differential equations on a graph. This result generalizes the previous one
obtained by the author to the case where the Hamiltonian $H$ admits a
degenerate critical point and, as a consequence, the graph may have segments
more than four at a node.