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.

中文翻译：

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对模拟活塞弹簧运动与粘性气体之间相互作用的系统进行分析

我们关注的是可压缩流体的一维流动，这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有弹簧。管道的另一侧是开放的——我们假设流入或流出边界条件。这种情况可以理解为人类肺部的玩具模型。我们解决了对上述过程进行建模的系统的唯一性和强解的存在性问题，特别强调了最大存在时间的估计。