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For optimal control problems with ordinary
differential equations where the -norm of the control is
minimized, often bang-bang principles hold. For systems that are
governed by a hyperbolic partial differential equation, the
situation is different:
even if a weak form of the bang-bang principle still holds for the wave equation,
it implies no restriction on the form of the optimal control.
To illustrate that
for the Dirichlet boundary control of the wave equation
in general not even feasible...
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