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About the controllability of two parabolic equations with first order terms in the coupling

De
55 pages
About the controllability of two parabolic equations with first order terms in the coupling. Luz DE TERESA in collaboration with A. Benabdallah, M. Cristofol, P. Gaitan IHP-CPDEA:Control of systems Paris; November 2010 LdeT Controllability of parabolic systems

  • coupled heat

  • a22 ·

  • ihp-cpdea

  • every initial

  • a11 y1

  • finite dimensional

  • kalman condition


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About the controllability of two parabolic equations with rst order terms in the coupling.
ERESA
LuzDET in collaboration with A. Benabdallah, M. Cristofol, P. Gaitan
IHP-CPDEA:Control of systems
Paris; November 2010
LdeTControllabilityofparabolicsystems
uocfdelptaehauqentColorotionsΩnTiΩTinonΣTΩinobarapfoytilibal
withaijLT)andAijLT)nforij=12. We say that system (1) isnull controllableif for every initial data 0 (y10y2)L2(Ω)there existsfL2(ωT)such that the corresponding solution of (1) satises
y1(T) =y2(T) =0
LetΩT= Ω×(0T),ωΩ. We consider (1) ty1= Δy1+a11y1+a12y2+A11 ∇y1+A12 ∇y2+fχω y1t(y2t=Δ=)yy22(+ta)21=y10+a22y2+A21 ∇y1+A22 ∇y2 y1(0) =y10()y2(0) =y20()
msteyscslitrolTConLde
Y=AY+Bu
THEOREM(KALMAN RANK CONDITION)
A∈ L(Rn),B∈ L(RmRn).
Kalman operator K:=BAB An1B∈ L(RnmRn)
ms
is controllable at timeT>0if and only if rank[A|B] =rankBAB An1B=n
ystelics
Ker(K) ={0}
Kalman condition is equivalent to
itinFEroweDO:kalonamfrimedsienlitylabiraboofpaLedrtloCTno
Y=DCA=00µ P
Kalman condition :
Ld
0 ν 0
ν6=µ
eTControl
11λB=
albilityofparabolicsyste
0 0 1 V
sm
Control
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the
heat
equation
LdeT
Controllability
of
parabolic
systems
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