## Abstract

This paper deals with the three-dimensional narrow escape problem in a dendritic spine shaped domain, which is composed of a relatively big head and a thin neck. The narrow escape problem is to compute the mean first passage time of Brownian particles traveling from inside the head to the end of the neck. The original model is to solve a mixed Dirichlet-Neumann boundary value problem for the Poisson equation in the composite domain, and is computationally challenging. In this paper we seek to transfer the original problem to a mixed Robin-Neumann boundary value problem by dropping the thin neck part, and rigorously derive the asymptotic expansion of the mean first passage time with high order terms. This study is a nontrivial three-dimensional generalization of the work in Li (2014 J. Phys. A: Math. Theor. 47 505202), where a two-dimensional analogue domain is considered.

Original language | English |
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Article number | 325203 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 50 |

Issue number | 32 |

DOIs | |

Publication status | Published - 14 Jul 2017 |

## Scopus Subject Areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

## User-Defined Keywords

- asymptotic analysis
- dendritic spine
- mean frst passage time
- mixed Robin-Neumann boundary value problem
- Narrow escape problem