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Fick's las selects the Neumann boundary condition
- Publication Year :
- 2023
-
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.<br />Comment: 22 pages, 5 figures
- Subjects :
- Mathematics - Analysis of PDEs
35K20, 35K57, 35K60, 82C24
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.00321
- Document Type :
- Working Paper