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This is a Quantitative Study study.

Steklov–Neumann Spectral Problem: Asymptotic Analysis and Applications to Diffusion-Controlled Reactions

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This analysis reveals spectral behavior in the Steklov problem and establishes implications for diffusion and first-passage processes.

The asymptotic behavior of the Steklov–Neumann spectral problem is derived, enhancing our understanding of diffusion processes.
Numerical results demonstrate the accuracy of asymptotic formulas for eigenvalues and eigenfunctions in specific geometries.
Applications of these spectral results to first-passage processes show the impact of surface reactions on reaction times.
The analysis leads to a universal function quantifying the effects of multiple failed reactions across various reactivities.

Denis S. Grebenkov (2025) studied this question.

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