Retour Groupe de Travail EDP et Théorie Spectrale
The Narrow escape problem in the unit disk
Salle de Conférences
le 17 mars 2023 à 11:00
In this talk, we investigate the Narrow escape problem in the unit disk, which is to find the first exit time and exit point for a Brownian particle confined within the unit disk with a reflecting boundary, except for small disjointed windows through which it can escape. This problem has practical applications in various fields. To solve this problem, we study the eigenvalue problem for the Laplacian operator with a Dirichlet boundary condition on a small absorbing part of the boundary and a Neumann boundary condition on the remaining reflecting part. We obtain rigorous asymptotic expansions of the first eigenvalue and the normal derivative of the associated eigenfunction.