Null controllability of a cascade system of parabolic-hyperbolic equations

This paper is concerned with the null controllability of a cascade linear system formed by a heat and a wave equation in a cylinder Omega x (0, T). The control acts only on the heat equation and is supported by a set of the form omega x (0, T), where w subset of Omega. In the wave equation, only the restriction of the solution to the heat equation to another set O x (0, T) appears. In the main result in this paper, we show that, under appropriate assumptions on T, omega and O, the system is null controllable.