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March  2004, 11(2&3): 699-714. doi: 10.3934/dcds.2004.11.699

Null controllability of a cascade system of parabolic-hyperbolic equations

Enrique Fernández-Cara 1, and  Luz de Teresa 2,

1. 

Dpto., E.D.A.N., Universidad de Sevilla, Aptdo. 1180; 41080 Sevilla, Spain
2. 

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico

Received  December 2002 Revised  February 2004 Published  June 2004

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.
Keywords: cascade system, parabolic-hyperbolic., Null controllability.
Mathematics Subject Classification: 93B05, 93B07, 93C20, 35M2.
Citation: Enrique Fernández-Cara, Luz de Teresa. Null controllability of a cascade system of parabolic-hyperbolic equations. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 699-714. doi: 10.3934/dcds.2004.11.699
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