Null controllability of degenerate parabolic operators with  drift

2007, Volume 2, Issue 4: 695-715. doi: 10.3934/nhm.2007.2.695

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1.
Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma
2.
Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Siena, Via Roma 56, 53100 Siena

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.
- Degenerate parabolic equations,
- null controllability,
- Carleman estimates,
- Hardy type inequality
Citation: Piermarco Cannarsa, Genni Fragnelli, Dario Rocchetti. Null controllability of degenerate parabolic operators with drift[J]. Networks and Heterogeneous Media, 2007, 2(4): 695-715. doi: 10.3934/nhm.2007.2.695

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Abstract

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.
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