Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type

Shuichi Jimbo, Masato Kimura, Hirofumi Notsu

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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 languageEnglish
Pages (from-to)103-123
Number of pages21
JournalAsymptotic Analysis
Issue number1-2
Publication statusPublished - 2009
Externally publishedYes



  • Asymptotic behaviour
  • Elliptic eigenvalue problems

ASJC Scopus subject areas

  • Mathematics(all)

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