ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - April 2013 - Volume 19, Issue 02  

Research Article

On time optimal control of the wave equation, its regularization and optimality system ∗

Karl Kunischa1 and Daniel Wachsmutha1

a1 Institute for Mathematics and Scientific Computing, Heinrichstraße 36, 8010 Graz, Austria. karl.kunisch@uni-graz.at; http://www.kfunigraz.ac.at/imawww/kunisch

a2 Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, 4040 Linz, Austria; daniel.wachsmuth@oeaw.ac.at; http://www.ricam.oeaw.ac.at/people/page/wachsmuth

Abstract

An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.

(Received March 20 2012)

(Revised February 23 2012)

(Online publication June 21 2012)

Key Words:

  • Time optimal control;
  • wave equation;
  • optimality condition;
  • transversality condition

Mathematics Subject Classification:

  • 49K20;
  • 93C20;
  • 35L05

Footnotes

∗  Partially supported by “Fonds zur Förderung der Wissenschaftlichen Forschung” under SFB 32, Mathematical Optimization and Applications in the Biomedical Sciences.