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

2008/02/08 by Shuichi Jimbo, Jimbo, Shuichi, Masato Kimura +3
Computer Science · Mathematics · #35B25 (Secondary) #47A75 (Primary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0802.1111

openalex publication_date 2008/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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