Abstract We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.

中文翻译：

---

输送粘性非牛顿流体的超弹性膜管的非线性稳态

摘要我们研究了由超弹性膜制成的无限长管的可能稳态，并通过幂律流变学输送无粘性或粘性流体。管模型在几何和物理上都是非线性的；流体模型仅限于管半径的平滑变化。对于无粘性情况，我们分析了管子的拉伸和流速范围，在该范围内存在膨胀型和颈缩型驻波。对于粘性情况，我们首先分析管的上游和下游极限状态，这些状态通过无限增加的上游（和减少下游）流体压力和流体粘度引起的轴向应力来平衡。然后我们研究可以通过单个解决方案连接这些极限状态的条件。我们证明了这样的解只存在于足够小的流速并且它具有扭结波的形式；孤立波不存在。对于半无限管（上游或下游无限）的情况，存在扭结和孤立波解。对于有限长度的管，存在任何类型的解，即以扭结波、孤立波和周期波的形式存在。