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 . We assume that the control is acting on an open subset , which is moving with a constant velocity . The main result of the paper shows that the equation is null controllable in a sufficiently large time 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.