An asymptotic analysis for Hamilton-Jacobi equations with large Hamiltonian drift terms

作者：Kumagai, Taiga^*

来源：Advances in Calculus of Variations, 2021, 14(1): 63-81.

DOI：10.1515/acv-2017-0046

• Singular perturbation
• Hamilton-Jacobi equations
• large drift
• graphs

We investigate the asymptotic behavior of solutions of Hamilton-jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by epsilon(-1)(H-x2,-H-x1) of a Hamiltonian 11, with epsilon > 0. We establish the convergence, as epsilon -> 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 more than four segments at a node.

• 出版日期2021-1