热方程中边界条件的出现

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-07-01 DOI:10.1063/5.0215656

Jaywan Chung, Seungmin Kang, Ho-Youn Kim, Yong-Jung Kim

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引用次数: 0

摘要

狄利克特条件和诺依曼条件通常被用作热方程的边界条件，但在某些情况下，它们的合理性值得商榷。本文旨在证明，事实上，扩散定律可以自主选择边界条件。为了说明这一点，我们将有界域并入一个更大的、具有扩散参数ϵ > 0 的域中，并研究了解在界面上的行为。我们的研究结果表明，当ϵ → 0 时，会出现同质 Neumann 或 Dirichlet 边界条件，这取决于异质扩散的类型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Emergence of boundary conditions in the heat equation

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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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.