Null-controllability properties of the wave equation with a second order memory term


Biccari U., Micu S. Null-controllability properties of the wave equation with a second order memory term, DOI:

Abstract: We study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus \mathbb{T}=\mathbb{R}/2\pi\mathbb{Z}. We assume that the control is acting on an open subset \omega(t)\subset\mathbb{T}, which is moving with a constant velocity c\in\mathbb{R}\setminus\{-1,0,1\}. The main result of the paper shows that the equation is null controllable in a sufficiently large time T and for initial data belonging to suitable Sobolev spaces. Its proof follows from a careful analysis of the spectrum associated to our problem and from the application of the classical moment method.

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