# On the reachable states for the boundary control of the heat equation

**Authors:**Ph. Martin, L.Rosier, P. Rouchon, Applied Mathematics Research eXpress, Vol. 2, pp.181-216, 16 September 2016 DOI: 10.1093/amrx/abv013

We are interested in the determination of the reachable states for the boundary control of the 1D heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable controls can be extended to analytic functions on some square of $ ${\mathbb C}$ $, and conversely, that analytic functions defined on a certain disk can be reached by using boundary controls that are Gevrey functions of order 2. The method of proof combines the flatness approach with some new Borel interpolation theorem in some Gevrey class with a specified value of the loss in the uniform estimates of the successive derivatives of the interpolating function.

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**BibTeX**

@Article{2016-11-26,

author = {L.Rosier Ph. Martin, P. Rouchon},

title = {On the reachable states for the boundary control of the heat equation},

journal = {Applied Mathematics Research eXpress},

volume = {2},

number = {},

pages = {181-216},

year = {2016},

}