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arXiv · 1807.03035

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

Umberto Biccari·Sorin Micu
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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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Umberto Biccari, Sorin Micu. 2018-07-09. Null-controllability properties of the wave equation with a second order memory term. https://arxiv.org/abs/1807.03035

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