Fick’s law selects the Neumann boundary condition

Hilhorst, Danielle; Kang, Seung-Min; Kim, Ho-Youn; Kim, Yong-Jung

doi:10.1016/j.na.2024.113561

Nonlinear Analysis

2024

DOI: 10.1016/j.na.2024.113561

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Fick’s law selects the Neumann boundary condition

Danielle Hilhorst,

Seung-Min Kang,

Ho-Youn Kim

et al.

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2024

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Emergence of boundary conditions in the heat equation

Chung,

Kang,

Kim

et al. 2024

Journal of Mathematical Physics

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The Dirichlet and Neumann conditions are commonly employed as boundary conditions for the heat equation, yet their legitimacy is debatable in certain scenarios. This paper aims to demonstrate that, in fact, diffusion laws autonomously select boundary conditions. To illustrate this, we incorporate the bounded domain into a larger domain with a diffusivity parameter ϵ > 0 and examine the solution’s behavior at the interface. Our findings reveal that homogeneous Neumann or Dirichlet boundary conditions emerge as ϵ → 0, contingent upon the type of the heterogeneous diffusion.

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Emergence of boundary conditions in the heat equation

Chung,

Kang,

Kim

et al. 2024

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

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Fick’s law selects the Neumann boundary condition

Cited by 1 publication

References 8 publications

Emergence of boundary conditions in the heat equation

Emergence of boundary conditions in the heat equation

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