活塞弹簧运动与粘性气体相互作用模型系统分析

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-13 DOI:10.1007/s10231-023-01386-z

Sabrine Chebbi, Václav Mácha, Šárka Nečasová

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引用次数: 0

摘要

我们关注的是可压缩流体的一维流动，它可以看作是细长管道中流体流动的简化。我们假设管道的一侧以弹簧为端点。管道的另一侧是开放的，我们假设这里有流入或流出的边界条件。这种情况可以理解为人类肺部的玩具模型。我们要解决的问题是，模拟上述过程的系统的唯一性和强解的存在性，特别强调对最大存在时间的估计。

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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Analysis of a system modeling the interaction between the motion of piston-spring and a viscous gas

We are concerned with a one-dimensional flow of a compressible fluid which may be seen as a simplification of the flow of fluid in a long thin pipe. We assume that the pipe is on one side ended by a spring. The other side of the pipe is let open—there we assume either inflow or outflow boundary conditions. Such situation can be understood as a toy model for human lungs. We tackle the question of uniqueness and existence of a strong solution for a system modeling the above process, special emphasis is laid upon the estimate of the maximal time of existence.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.