# American Institute of Mathematical Sciences

June  2013, 3(2): 121-142. doi: 10.3934/mcrf.2013.3.121

## Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws

 1 Applied Mathematics Division, University of Stellenbosch, Stellenbosch 7600, South Africa 2 RWTH Aachen University, IGPM, Templergraben 55, 52056 Aachen, Germany

Received  January 2012 Revised  January 2013 Published  March 2013

Suitable numerical discretizations for boundary control problems of systems of nonlinear hyperbolic partial differential equations are presented. Using a discrete Lyapunov function, exponential decay of the discrete solutions of a system of hyperbolic equations for a family of first--order finite volume schemes is proved. The decay rates are explicitly stated. The theoretical results are accompanied by computational results.
Citation: Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control & Related Fields, 2013, 3 (2) : 121-142. doi: 10.3934/mcrf.2013.3.121
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