Partial Differential Equations
Carleman estimates and null controllability for boundary-degenerate parabolic operators
Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 147-152.

Motivated by several examples coming from physics, biology, and economics, we consider a class of parabolic operators that degenerate at the boundary of the space domain. We study null controllability by a locally distributed control. For this purpose, a specific Carleman estimate for the solutions of degenerate adjoint problems is proved.

Motivés par de nombreux problèmes venant de la physique, la biologie et de l'économie, nous considérons une classe d'équations paraboliques dont l'opérateur associé dégénère au bord du domaine spatial. Nous étudions la nulle contrôlabilité, établissant en particulier une estimation de Carleman pour l'équation dégénérée adjointe.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.12.011
Cannarsa, Piermarco 1; Martinez, Partick 2; Vancostenoble, Judith 2

1 Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
2 Institut de mathématiques de Toulouse, U.M.R. C.N.R.S. 5219, Université Paul-Sabatier Toulouse III, 118, route de Narbonne, 31062 Toulouse cedex 4, France
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Cannarsa, Piermarco; Martinez, Partick; Vancostenoble, Judith. Carleman estimates and null controllability for boundary-degenerate parabolic operators. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 147-152. doi : 10.1016/j.crma.2008.12.011. http://www.numdam.org/articles/10.1016/j.crma.2008.12.011/

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