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September  2006, 5(3): 639-658. doi: 10.3934/cpaa.2006.5.639

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

 1 Dpto., E.D.A.N., Universidad de Sevilla, Aptdo. 1180; 41080 Sevilla 2 Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain 3 Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico

Received  April 2005 Revised  April 2006 Published  June 2006

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.
Citation: Enrique Fernández-Cara, Manuel González-Burgos, Luz de Teresa. Null-exact controllability of a semilinear cascade system of parabolic-hyperbolic equations. Communications on Pure and Applied Analysis, 2006, 5 (3) : 639-658. doi: 10.3934/cpaa.2006.5.639
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