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Null controllability of a cascade system of parabolic-hyperbolic equations

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  • This paper is concerned with the null controllability of a cascade linear system formed by a heat and a wave equation in a cylinder $\Omega \times (0,T)$. The control acts only on the heat equation and is supported by a set of the form $\omega \times (0,T)$, where $\omega \subset \Omega$. In the wave equation, only the restriction of the solution to the heat equation to another set $\mathcal O \times (0,T)$ appears. In the main result in this paper, we show that, under appropriate assumptions on $T$, $\omega$ and $\mathcal O$, the system is null controllable.
    Mathematics Subject Classification: 93B05, 93B07, 93C20, 35M20.

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