In this paper, we study the boundary feedback stabilization of a quasilinear hyperbolic system with partially dissipative structure. Thanks to this structure, we construct a suitable Lyapunov function which leads to the exponential stability to the equilibrium of the $H^2$ solution. As an application, we also obtain the feedback stabilization for the Saint-Venant-Exner model under physical boundary conditions.

中文翻译：

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具有部分耗散结构的拟线性双曲系统的边界反馈镇定

在本文中，我们研究了具有部分耗散结构的拟线性双曲系统的边界反馈镇定。由于这种结构，我们构建了一个合适的李雅普诺夫函数，它导致 $H^2$ 解的平衡的指数稳定性。作为应用，我们还获得了物理边界条件下 Saint-Venant-Exner 模型的反馈稳定性。