Classical solvability to the free boundary problem for a foam drainage equation. II. From the interface to the bottom

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-06 DOI:10.1063/5.0155457

Atusi Tani, Marie Tani

引用次数: 0

Abstract

We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. in 1988 in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region below an interface to the bottom in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle. Moreover, the existence of its steady solution and its stability are shown.

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泡沫排水方程自由边界问题的经典可解性。II.从界面到底部

我们研究的是描述一维情况下泡沫排水演变的非线性偏微分方程，该方程由 Goldfarb 等人于 1988 年提出，用于研究液体在重力和毛细管作用下流经气泡之间的通道（高原边界）和节点（四个通道的交叉点）的情况。迄今为止，对它的数学研究主要局限于数值解和特定解；至于数学分析，则寥寥无几。我们通过标准的经典数学方法--最大值原理，证明了泡沫排水方程在泡沫柱底部界面以下区域的自由边界问题具有唯一的全局时间经典解。此外，我们还证明了其稳定解的存在性和稳定性。

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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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.