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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Inverse problem and null-controllability for parabolic systems

1Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago, Casilla 307, Correo 2, Santiago, Chile.

2Institut Élie Cartan, UMR 7502, INRIA, Nancy-Université, CNRS, POB 239, Vandœuvre-lès-Nancy 54506, France.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 3, Pages 379–405, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.036, August 2011

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In this paper, we present some abstract results giving a general connection between null-controllability and several inverse problems for a class of parabolic equations. We obtain some conditional stability estimates for the inverse problems consisting of determining the initial condition and the source term, from interior or boundary measurements. We apply this framework for Stokes system with interior and boundary observations, for a coupling of two Stokes system and a linear fluid-structure system.

Keywords.: Inverse problem; controllability

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