In this work, we study the null-controllability properties of linear parabolic systems with constant coefficients in the case where several controls are acting on different distributed subdomains and/or on the boundary. We prove a Kalman rank condition in the one-dimensional case. In the case where only distributed controls are considered, we also establish related results such as a Carleman estimate.
Alabau-Boussouira F, Léautaud M (2011) Indirect controllability of locally coupled systems under geometric conditions. C R Acad Sci Paris 349(7–8): 395–400zbMATHGoogle Scholar
Ammar-Khodja F, Benabdallah A, Dupaix C (2006) Null-controllability of some reaction-diffusion systems with one control force. J Math Anal Appl 320(2): 928–943MathSciNetCrossRefGoogle Scholar
Ammar-Khodja F, Benabdallah A, Dupaix C, González-Burgos M (2009) A Kalman rank condition for the localized distributed controllability of a class of linear parbolic systems. J Evol Equ 1(2): 267–291CrossRefGoogle Scholar
Ammar-Khodja F, Benabdallah A, Dupaix C, González-Burgos M (2009) A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems. Differ Equ Appl 1(3): 139–151MathSciNetGoogle Scholar
Ammar-Khodja F, Benabdallah A, Dupaix C, Kostine I (2005) Null controllability of some systems of parabolic type by one control force. ESAIM Control Optim Calc Var 11(3): 426–448MathSciNetCrossRefGoogle Scholar
Imanuvilov OY, Yamamoto M (2003) Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations. Publ Res Inst Math Sci 39(2): 227–274MathSciNetzbMATHCrossRefGoogle Scholar
Tucsnak M, Weiss G (2009) Observation and control for operator semigroups, Advanced Texts, Birkhäuser, BaselGoogle Scholar