Observability for the Wave Equation with Variable Support in the Dirichlet and Neumann Cases
02 Pubblicazione su volume
Agresti Antonio, Andreucci Daniele, Loreti Paola
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.