Abstract:
In this dissertation, boundary stabilization of a linear hyperbolic system of balance laws is
considered. Of particular interest is the numerical boundary stabilization of such systems. An
analytical stability analysis of the system will be presented as a preamble. A discussion of
the application of the analysis on speci c examples: telegrapher equations, isentropic Euler
equations, Saint-Venant equations and Saint-Venant-Exner equations is also presented. The
rst order explicit upwind scheme is applied for the spatial discretization. For the temporal
discretization a splitting technique is applied. A discrete 𝕃 ²−Lyapunov function is employed
to investigate conditions for the stability of the system. A numerical analysis is undertaken and
convergence of the solution to its equilibrium is proved. Further a numerical implementation
is presented. The numerical computations also demonstrate the stability of the numerical
scheme with parameters chosen to satisfy the stability requirements.
