### Abstract

We study an asymptotic behaviour of the principal eigenvalue for an elliptic operator with large advection which is given by a gradient of a potential function. It is shown that the principal eigenvalue decays exponentially under the velocity potential well condition as the parameter tends to infinity. We reveal that the depth of the potential well plays an important role in the estimate. Particularly, in one-dimensional case, we give a much more elaborate characterization for the eigenvalue. Some numerical examples are also shown.

Original language | English |
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Pages (from-to) | 103-123 |

Number of pages | 21 |

Journal | Asymptotic Analysis |

Volume | 65 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

### Keywords

- Asymptotic behaviour
- Elliptic eigenvalue problems

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Jimbo, S., Kimura, M., & Notsu, H. (2009). Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type.

*Asymptotic Analysis*,*65*(1-2), 103-123. https://doi.org/10.3233/ASY-2009-0951