Emergence of boundary conditions in the heat equation

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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 & varepsilon; > 0 and examine the solution's behavior at the interface. Our findings reveal that homogeneous Neumann or Dirichlet boundary conditions emerge as & varepsilon; -> 0, contingent upon the type of the heterogeneous diffusion.
Publisher
AIP Publishing
Issue Date
2024-07
Language
English
Article Type
Article
Citation

JOURNAL OF MATHEMATICAL PHYSICS, v.65, no.7

ISSN
0022-2488
DOI
10.1063/5.0215656
URI
http://hdl.handle.net/10203/322941
Appears in Collection
MA-Journal Papers(저널논문)
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