Asymptotic Analysis for the Narrow Escape Problem

摘要: Consider a domain whose boundary is reflecting, except for finite number of absorbing sets (“windows”) with small radius. The narrow escape problem concerned estimating the expected time that it takes Brownian particle initially inside to reach one windows and thus exit from domain; when hits at any point which not in windows, reflected back into domain. motivated, example, by protein, or other molecule cytoplasm cell, moves randomly until cell membrane channels enable cell. In this paper we derive rigorous mathematical analysis asymptotic estimates on time, up order size windows.