Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach
- 1.7k Downloads
n this paper we summarize our recent results on the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. It is shown that the projection of the solution in an appropriate space in which the high frequencies have been filtered is exactly controllable with uniformly bounded controls (with respect to the time-step). By classical duality arguments, the problem is reduced to a boundary observability inequality for a time-discrete wave equation. Using multiplier techniques the uniform observability property is proved in a class of filtered initial data. The optimality of the filtering parameter is also analyzed.
Key wordsExact controllability observability time discretization wave equation multiplier technique filtering.
Unable to display preview. Download preview PDF.
- 6.J.-L. Lions. Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Vol. 1. Masson, Paris, 1988.Google Scholar
- 7.F. Macià. The effect of group velocity in the numerical analysis of control problems for the wave equation. In Mathematical and Numerical Aspects of Wave Propagation – WAVES 2003, pages 195–200, Berlin, 2003. Springer.Google Scholar