# Boundary Control of PDEs via Curvature Flows: the View from the Boundary, II

Boundary Control of PDEs via Curvature Flows: the View from the Boundary, II 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Boundary Control of PDEs via Curvature Flows: the View from the Boundary, II

, Volume 46 (3) – Dec 19, 2002
12 pages

/lp/springer_journal/boundary-control-of-pdes-via-curvature-flows-the-view-from-the-IzbO932vo7
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-002-0742-6
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 19, 2002

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