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Pré-Publication, Document De Travail Année : 2011

The uniform controllability property of semidiscrete approximations for the parabolic distributed parameter systems in Banach spaces.

Résumé

The problem we consider in this work is to minimize the L^q-norm (q > 2) of the semidiscrete controls. As shown in [LT06], under the main approximation assumptions that the discretized semigroup is uniformly analytic and that the degree of unboundedness of control operator is lower than 1/2, the uniform controllability property of semidiscrete approximations for the parabolic systems is achieved in L^2. In the present paper, we show that the uniform controllability property still continue to be asserted in L^q. (q > 2) even with the con- dition that the degree of unboundedness of control operator is greater than 1/2. Moreover, the minimization procedure to compute the ap- proximation controls is provided. An example of application is imple- mented for the one dimensional heat equation with Dirichlet boundary control.
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Dates et versions

hal-00591000 , version 1 (06-05-2011)
hal-00591000 , version 2 (08-05-2011)
hal-00591000 , version 3 (29-05-2011)
hal-00591000 , version 4 (24-06-2011)

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Thuy Nguyen. The uniform controllability property of semidiscrete approximations for the parabolic distributed parameter systems in Banach spaces.. 2011. ⟨hal-00591000v4⟩
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