Piermarco Cannarsa, Luz de Teresa
Abstract:
This article is devoted to the study of null controllability
properties for two systems of coupled one dimensional
degenerate parabolic equations. The first system consists
of two forward equations, while the second one consists
of one forward equation and one backward equation.
Both systems are in cascade, that is, the solution of the first
equation acts as a control for the second equation and the
control function only acts directly in the first equation.
We prove positive null controllability results when the
control and coupling sets have nonempty intersection and 0
does not belong to the coupling set.
Submitted October 21, 2008. Published June 3, 2009.
Math Subject Classifications: 35K65, 93C20.
Key Words: Degenerate parabolic systems; controllability.
An addendum was posted on October 10, 2016. It gives a Carleman inequality to be used in the correct proofs of Theorems 1.1 and 1.2. See the last four pages of this article.
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Piermarco Cannarsa Dipartimento di Matematica Universitá di Roma "Tor Vergata" 00133, Roma, Italy email: cannarsa@mat.uniroma2.it |
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Luz de Teresa Instituto de Matemáticas Universidad Nacional Autónoma de México Circuito Exterior, C.U., C. P. 04510 D.F., Mexico email: deteresa@matem.unam.mx |
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