Null controllability of a cascade system of parabolic-hyperbolic equations

Enrique Fernández-Cara; Luz de Teresa

doi:10.3934/dcds.2004.11.699

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2004, Volume 11, Issue 2&3: 699-714. Doi: 10.3934/dcds.2004.11.699

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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
2.
Instituto de Matemáticas, Universidad Nacional Autónoma de México

Received: November 30, 2002

Revised: January 31, 2004

Published: August 2004

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Abstract

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.

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Mathematics Subject Classification: 93B05, 93B07, 93C20, 35M20.

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