下降不可扩展网络的过阻尼动力学:解的存在性

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2022-01-14 DOI:10.4171/ifb/492

Ayk Telciyan, D. Vorotnikov

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引用次数: 0

摘要

研究了在重力作用下具有三个固定端和一个自由结的不可扩展三角的过阻尼运动方程。该问题可以表示为一个包含未知拉格朗日乘子和与自由移动结相关的非标准边界条件的偏微分方程系统。它也可以正式地解释为概率测度的Otto-Wasserstein空间的某一子流形上势能的梯度流。我们证明了这个问题的广义解的整体存在性。

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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Overdamped dynamics of a falling inextensible network: Existence of solutions

We study the equations of overdamped motion of an inextensible triod with three fixed ends and a free junction under the action of gravity. The problem can be expressed as a system of PDE that involves unknown Lagrange multipliers and non-standard boundary conditions related to the freely moving junction. It can also be formally interpreted as a gradient flow of the potential energy on a certain submanifold of the Otto-Wasserstein space of probability measures. We prove global existence of generalized solutions to this problem.

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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.