Electron. J. Diff. Eqns., Vol. 2009(2009), No. 73, pp. 1-21.

Controllability of 1-d coupled degenerate parabolic equations

Piermarco Cannarsa, Luz de Teresa

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
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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