Domain Decomposition in Optimal Final Value Control of Dissipative Wave Equations

  • John E. Lagnese
  • Günter Leugering
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 148)


This chapter is concerned with domain decomposition methods for the computation of the solution of the optimality system associated with final value optimal control of second-order hyperbolic equations in which the control action enters through a dissipative boundary condition. More specifically, we consider optimal final value control of solutions of hyperbolic systems of the form
$$ \begin{gathered} \frac{{\partial ^2 w}} {{\partial t^2 }} - \nabla \cdot (A\nabla w) + cw = F in Q: = \Omega \times (0,T) \hfill \\ w = 0 on \Sigma ^D : = \Gamma ^D \times (0,T) \hfill \\ \frac{{\partial w}} {{\partial \nu _A }} + \alpha \frac{{\partial w}} {{\partial t}} = f on \Sigma ^N : = \Gamma ^N \times (0,T) \hfill \\ w(0) = w_0 , \frac{{\partial w}} {{\partial t}}(0) = v_0 in \Omega \hfill \\ \end{gathered} $$


Optimal Control Problem Spatial Domain Optimality System Domain Decomposition Posteriori Error Estimate 
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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • John E. Lagnese
    • 1
  • Günter Leugering
    • 2
  1. 1.Department of MathematicsGeorgetown UniversityUSA
  2. 2.Angewandte Mathematik IIUniversität Erlangen NürnbergErlangenGermany

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