Null controllability of a cascade system of parabolic-hyperbolic equations

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February & 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

Abstract
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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.

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

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