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Null-exact controllability of a semilinear cascade system of parabolic-hyperbolic equations

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  • This paper is concerned with the null-exact controllability of a cascade system formed by a semilinear heat and a semilinear wave equation in a cylinder $\Omega \times (0,T)$. More precisely, we intend to drive the solution of the heat equation (resp. the wave equation) exactly to zero (resp. exactly to a prescribed but arbitrary final state). 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, the restriction of the solution to the heat equation to another set $\mathcal O \times (0,T)$ appears. The nonlinear terms are assumed to be globally Lipschitz-continuous. In the main result in this paper, we show that, under appropriate assumptions on $T$, $\omega$ and $\mathcal O$, the equations are simultaneously controllable.
    Mathematics Subject Classification: 35M20, 93B05, 93B07.


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