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March  2017, 7(1): 21-40. doi: 10.3934/mcrf.2017002

## Construction of gevrey functions with compact support using the bray-mandelbrojt iterative process and applications to the moment method in control theory

 Ceremade, Université Paris-Dauphine & CNRS, UMR 7534, PSL, 75016 Paris, France

* Corresponding author: Pierre Lissy

Received  December 2015 Revised  October 2016 Published  December 2016

In this paper, we construct some interesting Gevrey functions of order $α$ for every $α>1$ with compact support by a clever use of the Bray-Mandelbrojt iterative process. We then apply these results to the moment method, which will enable us to derive some upper bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type that partially improve the existing results proved in [P. Lissy, On the Cost of Fast Controls for Some Families of Dispersive or Parabolic Equations in One Space Dimension SIAM J. Control Optim., 52(4), 2651-2676]. However this construction fails to improve the results of [G. Tenenbaum and M. Tucsnak, New blow-up rates of fast controls for the Schrödinger and heat equations, Journal of Differential Equations, 243 (2007), 70-100] in the precise case of the usual heat and Schrödinger equation.

Citation: Pierre Lissy. Construction of gevrey functions with compact support using the bray-mandelbrojt iterative process and applications to the moment method in control theory. Mathematical Control & Related Fields, 2017, 7 (1) : 21-40. doi: 10.3934/mcrf.2017002
##### References:

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##### References:
Difference between $C_S(\alpha)$ and the upper bound of [11] with respect to $\alpha$
Difference between $C_S(\alpha)$ and the lower bound of [12] with respect to $\alpha$
Difference between $C_H(\alpha)$ and the upper bound of [11] with respect to $\alpha$
Difference between $C_H(\alpha)$ and the lower bound of [12] with respect to $\alpha$
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