FLATNESS APPROACH FOR THE BOUNDARY CONTROLLABILITY OF A SYSTEM OF HEAT EQUATIONS.

We study the boundary controllability of 2×2 system of heat equations by using a flatness approach. According to the relation between the diffusion coefficients of the heat equation, it is known that the system can be neither null-controllable nor null-controllable for any T>T₀, where T₀∈[0,∞]. Here we recover this result in the case that T₀∈[0,∞) by using the flatness method, and we obtain an explicit formula for the control and for the corresponding solutions. In particular, the state and the control have Gevrey regularity in time and in space. [ABSTRACT FROM AUTHOR]