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Applied Mathematics Research eXpress (2006) Vol. 2006 : article ID 75090, 31 pages, doi:10.1155/AMRX/2006/75090
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Global Carleman estimates for solutions of parabolic systems defined by transposition and some applications to controllability

Enrique Fernández-Cara and Sergio Guerrero

Department of Differential Equations and Numerical Analysis, University of Sevilla P.O. Box 1160, 41080 Sevilla, Spain E-mail address: cara{at}us.es
Jacques-Louis Lions Laboratory, University Pierre and Marie Curie (Paris 6) P.O. Box 187, 75252 Paris Cedex 05, France E-mail address: guerrero{at}ann.jussieu.fr

We establish several controllability results for some nonlinear parabolic systems where the nonlinearity affects the time derivative and/or the second-order spatial derivatives. The main tool is a new Carleman estimate that holds for very weak solutions to linear parabolic systems.


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