### Abstract

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 ϵ - 1 ( H x 2 , - H x 1 ) ^{-1}(H_{2},-H_{x}1) of a Hamiltonian H, with ϵ > 0 >0 . We establish the convergence, as ϵ → 0 + 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 more than four segments at a node.

Original language | English |
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Journal | Unknown Journal |

DOIs | |

Publication status | Accepted/In press - 2017 Nov 14 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Unknown Journal*. https://doi.org/10.1515/acv-2017-0046

**An asymptotic analysis for Hamilton-Jacobi equations with large Hamiltonian drift terms.** / Kumagai, Taiga.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An asymptotic analysis for Hamilton-Jacobi equations with large Hamiltonian drift terms

AU - Kumagai, Taiga

PY - 2017/11/14

Y1 - 2017/11/14

N2 - 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 ϵ - 1 ( H x 2 , - H x 1 ) -1(H2,-Hx1) of a Hamiltonian H, with ϵ > 0 >0 . We establish the convergence, as ϵ → 0 + 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 more than four segments at a node.

AB - 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 ϵ - 1 ( H x 2 , - H x 1 ) -1(H2,-Hx1) of a Hamiltonian H, with ϵ > 0 >0 . We establish the convergence, as ϵ → 0 + 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 more than four segments at a node.

KW - graphs

KW - Hamilton-Jacobi equations

KW - large drift

KW - Singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=85037695482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037695482&partnerID=8YFLogxK

U2 - 10.1515/acv-2017-0046

DO - 10.1515/acv-2017-0046

M3 - Article

AN - SCOPUS:85037695482

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -