Asymptotic analysis for Hamilton-Jacobi equations with large drift term

2017/05/04 by Taiga Kumagai, Kumagai, Taiga
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1705.01933

openalex publication_date 2017/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ε^-1 (H_x2, -H_x1) of a Hamiltonian H, with ε > 0, we establish the convergence, as ε → 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.

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