交汇点处2x2双曲守恒律方程组熵解的反馈镇定
Feedback stabilization for entropy solutions of a 2x2 hyperbolic system of conservation laws at a junction
AI总结：
本文研究了星形网络上p-system的反馈镇定问题，通过扩展Coron等人的策略并利用front-tracking算法与指数加权Glimm型Lyapunov泛函控制BV范数，证明了在适当条件下系统的熵解是指数可镇定的。
摘要：
我们在星形网络上考虑Eulerian坐标下的p-system。在交汇点处适当的传输条件和外部顶点处的耗散边界条件下，我们证明了该系统的熵解是指数可镇定的。我们的证明扩展了Coron等人（2017）的策略，并基于front-tracking算法构造近似分片常数解，其BV范数通过适当的指数加权Glimm型Lyapunov泛函来控制。
英文摘要：
We consider the p-system in Eulerian coordinates on a star-shaped network. Under suitable transmission conditions at the junction and dissipative boundary conditions in the exterior vertices, we show that the entropy solutions of the system are exponentially stabilizable. Our proof extends the strategy by Coron et al. (2017) and is based on a front-tracking algorithm used to construct approximate piecewise constant solutions whose BV norms are controlled through a suitable exponentially-weighted Glimm-type Lyapunov functional.
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