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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)103-123
Number of pages21
JournalAsymptotic Analysis
Volume65
Issue number1-2
DOIs
Publication statusPublished - 2009
Externally publishedYes

Fingerprint

Principal Eigenvalue
Potential Well
Exponential Decay
Elliptic Operator
Gradient
Term
Advection
Potential Function
Asymptotic Behavior
Infinity
Decay
Tend
Eigenvalue
Numerical Examples
Estimate

Keywords

  • Asymptotic behaviour
  • Elliptic eigenvalue problems

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type. / Jimbo, Shuichi; Kimura, Masato; Notsu, Hirofumi.

In: Asymptotic Analysis, Vol. 65, No. 1-2, 2009, p. 103-123.

Research output: Contribution to journalArticle

Jimbo, Shuichi ; Kimura, Masato ; Notsu, Hirofumi. / Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type. In: Asymptotic Analysis. 2009 ; Vol. 65, No. 1-2. pp. 103-123.
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