### Abstract

We study the asymptotic behavior of solutions of the Cauchy problem for a functional partial differential equation with a small parameter as the parameter tends to zero. We establish a convergence theorem in which the limit problem is identified with the Cauchy problem for a nonlinear parabolic partial differential equation. We also present comparison and existence results for the Cauchy problem for the functional partial differential equation and the limit problem.

Original language | English |
---|---|

Pages (from-to) | 409-438 |

Number of pages | 30 |

Journal | Communications in Partial Differential Equations |

Volume | 28 |

Issue number | 1-2 |

Publication status | Published - 2003 |

### Fingerprint

### Keywords

- Hamiton-Jacobi equations
- Infinite system
- Perturbed test functions
- Singular limit
- Viscosity solutions

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics

### Cite this

*Communications in Partial Differential Equations*,

*28*(1-2), 409-438.

**Asymptotic analysis for a class of infinite systems of first-order PDE : Nonlinear parabolic PDE in the singular limit.** / Ishii, Hitoshi; Shimano, Kazufumi.

Research output: Contribution to journal › Article

*Communications in Partial Differential Equations*, vol. 28, no. 1-2, pp. 409-438.

}

TY - JOUR

T1 - Asymptotic analysis for a class of infinite systems of first-order PDE

T2 - Nonlinear parabolic PDE in the singular limit

AU - Ishii, Hitoshi

AU - Shimano, Kazufumi

PY - 2003

Y1 - 2003

N2 - We study the asymptotic behavior of solutions of the Cauchy problem for a functional partial differential equation with a small parameter as the parameter tends to zero. We establish a convergence theorem in which the limit problem is identified with the Cauchy problem for a nonlinear parabolic partial differential equation. We also present comparison and existence results for the Cauchy problem for the functional partial differential equation and the limit problem.

AB - We study the asymptotic behavior of solutions of the Cauchy problem for a functional partial differential equation with a small parameter as the parameter tends to zero. We establish a convergence theorem in which the limit problem is identified with the Cauchy problem for a nonlinear parabolic partial differential equation. We also present comparison and existence results for the Cauchy problem for the functional partial differential equation and the limit problem.

KW - Hamiton-Jacobi equations

KW - Infinite system

KW - Perturbed test functions

KW - Singular limit

KW - Viscosity solutions

UR - http://www.scopus.com/inward/record.url?scp=0038107449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038107449&partnerID=8YFLogxK

M3 - Article

VL - 28

SP - 409

EP - 438

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 1-2

ER -