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December  2007, 2(4): 695-715. doi: 10.3934/nhm.2007.2.695

Null controllability of degenerate parabolic operators with drift

Piermarco Cannarsa 1, , Genni Fragnelli 2, and  Dario Rocchetti 1,

1. 

Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy
2. 

Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Siena, Via Roma 56, 53100 Siena

Received  June 2007 Revised  September 2007 Published  September 2007

We give null controllability results for some degenerate parabolic equations in non divergence form with a drift term in one space dimension. In particular, the coefficient of the second order term may degenerate at the extreme points of the space domain. For this purpose, we obtain an observability inequality for the adjoint problem using suitable Carleman estimates.
Keywords: Carleman estimates, Degenerate parabolic equations, null controllability, Hardy type inequality.
Mathematics Subject Classification: Primary: 93B05, 93C20, 93B07; Secondary: 35K6.
Citation: Piermarco Cannarsa, Genni Fragnelli, Dario Rocchetti. Null controllability of degenerate parabolic operators with drift. Networks & Heterogeneous Media, 2007, 2 (4) : 695-715. doi: 10.3934/nhm.2007.2.695
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