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On the null controllability of a 3×3 parabolic system with non-constant coefficients by one or two control forces

Abstract : This work is concerned with the null controllability of a class of 3×3 linear parabolic systems with non-constant coefficients by a single control force or two control forces localized in space. We extend to this class of systems the Kalman rank condition existing for systems with constant or time-dependent coefficients. To prove the result, we construct a solution to the controllability issue using a suitable decomposition. With this decomposition, we are led to study the null controllability of either a non-homogeneous system of two equations by one control force acting on the whole domain (in the case of one distributed control force for the initial 3×3 system), or a non-homogeneous equation by two forces acting in the whole domain (in the case of two distributed control forces for the 3×3 system).
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Karine Mauffrey. On the null controllability of a 3×3 parabolic system with non-constant coefficients by one or two control forces. Journal de Mathématiques Pures et Appliquées, Elsevier, 2012, 99 (2), pp.187-210. ⟨10.1016/j.matpur.2012.06.010⟩. ⟨hal-00864253⟩

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