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- W2964972229 abstract "We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but also to require the memory term to vanish at the same time, ensuring that the whole process reaches the equilibrium. The problem being equivalent to a coupled nonlocal PDE-ODE system, in which the ODE component has zero velocity of propagation, we are required to use a moving control strategy. Assuming that the control is acting on an open subset $ omega(t) $ which is moving with a constant velocity $ cinmathbb{R} $, the main result of the paper states that the equation is null controllable in a sufficiently large time $ T $ and for initial data belonging to suitable fractional order Sobolev spaces. The proof will use a careful analysis of the spectrum of the operator associated with the system and an application of a classical moment method." @default.
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- W2964972229 date "2020-01-01" @default.
- W2964972229 modified "2023-10-14" @default.
- W2964972229 title "Null-controllability properties of a fractional wave equation with a memory term" @default.
- W2964972229 doi "https://doi.org/10.3934/eect.2020011" @default.
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