Boundary feedback stabilization of quasilinear hyperbolic systems with partially dissipative structure

2020/03/29 by Ke Wang, Zhiqiang Wang, Wang, Ke +3
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2003.12942

Abstract

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 H² solution. As an application, we also obtain the feedback stabilization for the Saint-Venant-Exner model under physical boundary conditions.

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