We consider a mathematical model for the gas flow through a one-way valve and focus on two issues. First, we propose a way to eliminate the chattering (the fast switch on and off of the valve) by slightly modifying the design of the valve. This mathematically amounts to the construction of a coupling Riemann solver with a suitable stability property, namely, coherence. We provide a numerical comparison of the behavior of the two valves. Second, we analyze, both analytically and numerically, for several significative situations, the maximization of the flow through the modified valve according to a control parameter of the valve and time.

翻译：我们考虑一个单向阀门气流的数学模型,并关注两个问题。 首先,我们提出一种方法,通过对阀门的设计略微修改来消除闲聊(开关和关闭阀门的快速开关),这在数学上相当于建造一个连接的里曼解答器,具有适当的稳定性属性,即一致性。我们对两个阀门的行为进行数字比较。 其次,我们从分析的角度和数字的角度分析若干具有标志性的情况,根据阀门的控制参数和时间,通过经修改的阀门的流量最大化。