SINGULAR PERTURBATION APPROACH TO KRAMER'S DIFFUSION PROBLEM.

B. J. Matkowsky*, Z. Schuss, E. Ben-Jacobs

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

81 Scopus citations

Abstract

This study considers Kramers' diffusion problem, which seeks to calculate the rate of escape of a particle from one potential well over a barrier, to another presumably deeper and therefore more stable well. A new approach, based on the solution of a singularly perturbed boundary value problem is proposed. The rate of escape is related to the first passage time from the domain of attraction of the stable point corresponding to the first well. The first passage time is then characterized via the Ito calculus, as a solution of an elliptic partial differential equation of singular perturbation type. Finally this equation is solved asymptotically.

Original languageEnglish (US)
Pages (from-to)835-849
Number of pages15
JournalSIAM Journal on Applied Mathematics
Volume42
Issue number4
DOIs
StatePublished - Jan 1 1982

ASJC Scopus subject areas

  • Applied Mathematics

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