Abstract
We describe some results on the exact boundary controllability of the wave equation on an orientable two-dimensional Riemannian manifold with nonempty boundary. If the boundary has positive geodesic curvature, we show that the problem is controllable in finite time if (and only if) there are no closed geodesics in the interior of the manifold. This is done by solving a parabolic problem to construct a convex function. We exhibit an example for which control from a subset of the boundary is possible, but cannot be proved by means of convex functions. We also describe a numerical implementation of this method.
Original language | English (US) |
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Pages (from-to) | 167-178 |
Number of pages | 12 |
Journal | Applied Mathematics and Optimization |
Volume | 46 |
Issue number | 2-3 |
DOIs | |
State | Published - Sep 2002 |
Keywords
- Boundary control
- Curvature flow
- Pseudoconvex function
- Riemannian manifold
- Wave equation