The uniform controllability property of semidiscrete approximations for the parabolic distributed parameter systems in Banach spaces
Abstract
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.
Keywords
Cite
@article{arxiv.1106.4988,
title = {The uniform controllability property of semidiscrete approximations for the parabolic distributed parameter systems in Banach spaces},
author = {Thuy Nguyen},
journal= {arXiv preprint arXiv:1106.4988},
year = {2011}
}