Internal controllability of parabolic systems with star and tree like couplings

Internal controllability of parabolic systems with star and tree like couplings

We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of the system, under hypotheses concerning the supports of the c...

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Veröffentlicht in:arXiv.org 2021-12
Hauptverfasser: Catalin-George Lefter, Elena-Alexandra Melnig
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Controllability
Couplings
Mathematical analysis
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description We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of the system, under hypotheses concerning the supports of the coupling functions. The key point is establishing Carleman estimates with appropriate observation operators for the adjoint to the linearized system, which allows the study of the controllability problem, in either linear or nonlinear cases, in an \(L^\infty\) framework.
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subjects Controllability
Couplings
Mathematical analysis
title Internal controllability of parabolic systems with star and tree like couplings
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