### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Asymptotic analysis for a class of infinite systems of first-order PDE: Nonlinear parabolic PDE in the singular limit'. Together they form a unique fingerprint.

## Cite this

Ishii, H., & Shimano, K. (2003). Asymptotic analysis for a class of infinite systems of first-order PDE: Nonlinear parabolic PDE in the singular limit.

*Communications in Partial Differential Equations*,*28*(1-2), 409-438.