Boundary control of PDEs via curvature flows: The view from the boundary, II

Santiago Betelú, Robert D Gulliver, Walter Littman

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 languageEnglish (US)
Pages (from-to)167-178
Number of pages12
JournalApplied Mathematics and Optimization
Volume46
Issue number2-3
DOIs
StatePublished - Sep 1 2002

Keywords

  • Boundary control
  • Curvature flow
  • Pseudoconvex function
  • Riemannian manifold
  • Wave equation

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