2020/06/03 by Mapundi K. Banda, Banda, Mapundi Kondwani, Gediyon Weldegiyorgis +1
Engineering · Mathematics · Computer Science · #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2006.04553
A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an input-to-state-stability (ISS) L2- Lyapunov function, the decay of solutions of linear systems of balance laws is proved. In the discrete framework, a first-order finite volume scheme is employed. In such cases, the decay rates can be explicitly derived. The main objective is to prove the Lyapunov stability for the L2-norm for linear hyperbolic systems of balance laws with additive disturbance both analytically and numerically. Theoretical results are demonstrated by using numerical computations.