Characterization of the Mean First-Passage Time Function Subject to Advection in Annular-like Domains

Hélia Serrano () and Ramón F. Álvarez-Estrada
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Hélia Serrano: Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
Ramón F. Álvarez-Estrada: Departamento de Física Teórica, Facultad de Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain

Mathematics, 2023, vol. 11, issue 24, 1-17

Abstract: Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by assumption a diffusion–advection equation that is subject to a Dirichlet boundary condition on the outer boundary and a Robin boundary condition on the inner boundary. The mean first-passage time (MFPT) function determined by u estimates the average time for the travelling cell to reach various interesting targets. The MFPT function fulfills a Poisson equation inside a domain with suitable boundary conditions, which give rise to various mathematical problems. The main novelty of this study is the characterization of such an MFPT function inside an annulus and an annular cylinder, which is subject to a Robin boundary condition on the inner boundary and a Dirichlet boundary condition on the outer one, and these are integral functions whose densities are the solution of an inhomogeneous system of linear integral equations.

Keywords: mean first-passage time; diffusion–advection equation; Dirichlet and Robin boundary conditions; annulus; annular cylinder (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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