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Mixed Steklov-Neumann problem: asymptotic analysis and applications to diffusion-controlled reactions
- Publication Year :
- 2024
-
Abstract
- Many first-passage processes in complex media and related diffusion-controlled reactions can be described by means of eigenfunctions of the mixed Steklov-Neumann problem. In this paper, we investigate this spectral problem in a common setting when a small target or escape window (with Steklov condition) is located on the reflecting boundary (with Neumann condition). We start by inspecting two basic settings: an arc-shaped target on the boundary of a disk and a spherical-cap-shaped target on the boundary of a ball. We construct the explicit kernel of an integral operator that determines the eigenvalues and eigenfunctions and deduce their asymptotic behavior in the small-target limit. By relating the limiting kernel to an appropriate Dirichlet-to-Neumann operator, we extend these asymptotic results to other bounded domains with smooth boundaries. A straightforward application to first-passage processes is presented; in particular, we revisit the small-target behavior of the mean first-reaction time on perfectly or partially reactive targets, as well as for more sophisticated surface reactions that extend the conventional narrow escape problem.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.00213
- Document Type :
- Working Paper