Prof. Dr. Mapundi Banda - A Lyapunov Approach to Boundary Feedback Stabilisation for Hyperbolic Balance Laws: a Numerical Perspective

Department for Mathematics and Applied Mathematics, University of Pretoria, South Africa

Abstract

First-order systems of evolution models governed by time-dependent hyperbolic partial dierential equations will be considered. In this talk we will present a review of the Lyapunov approach for boundary feedback stabilisation for such dierential equations. The rst part of the presentation will give an overview of recent results in the mathematical analysis of stabilisation of hyperbolic balance laws. The second part will then discuss a numerical approach to discretise the balance laws. This will be followed by a numerical analysis for the discrete Lyapunov approach. A selection of examples will be discussed and the eectiveness of the numerical stabilisation will also be demonstrated.