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arXiv · 2308.00321

Fick's las selects the Neumann boundary condition

Danielle Hilhorst·Seung-Min Kang·Ho-Youn Kim·Yong-Jung Kim
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Abstract

We study the appearance of a boundary condition along an interface between two regions, one with constant diffusivity $1$ and the other with diffusivity $\eps>0$, when $\eps\to0$. In particular, we take Fick's diffusion law in a context of reaction-diffusion equation with bistable nonlinearity and show that the limit of the reaction-diffusion equation satisfies the homogeneous Neumann boundary condition along the interface. This problem is developed as an application of heterogeneous diffusion laws to study the geometry effect of domain.

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Danielle Hilhorst, Seung-Min Kang, Ho-Youn Kim, Yong-Jung Kim. 2023-08-01. Fick's las selects the Neumann boundary condition. https://arxiv.org/abs/2308.00321

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