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

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

Authors

Jimbo, Shuichi

Kimura, Masato

Notsu, Hirofumi

Description

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.
25 pages, 24 figures