We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof of the observability inequality, which is proven by a multiplier method. Besides our main results, we present some applications.
We study the observability of the wave equation when the
observation set changes over time.
For the one dimensional Neumann problem, using Fourier series, we
are able to prove for the exact observability an equivalent condition
already known for the Dirichlet problem; see [1].
For the observability problem with Dirichlet boundary conditions, we
focus on multidimensional problems and the observability inequality is
proven through a multiplier approach.
Besides this, we present some applications and a numerical simulation.
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