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摘要
We address in this work the minimization of the L-q-norm (q > 2) of semidiscrete controls for parabolic equation. As shown in [15], 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, uniform controllability is achieved in L-2 for semidiscrete approximations for the parabolic systems. The main goal of this paper is to overcome the limitation of [15] about the order 1/2 of unboundedness of the control operator. Namely, we show that the uniform controllability property also holds in L-q (q > 2) even in the case of a degree of unboundedness greater than 1/2. Moreover, a minimization procedure to compute the approximation controls in L-q (q > 2) is provided. An example of application is implemented for the one-dimensional heat equation with Dirichlet boundary control.
- 出版日期2015-3
