| Abstract: |
| Recently, the issue of the determination of the reachable states for the boundary control of the one-dimensional heat equation has been revisited by several approaches. After a brief review of these results, we will discuss some recent extensions: (i) the derivation of the exact controllability of some nonlinear parabolic equations, including the viscous Burgers equation and the Allen-Cahn equation) (ii) the investigation of the reachable spaces of the Korteweg-de Vries equation with a control from the left endpoint. The above results are obtained in some spaces of analytic functions, and the analysis involves some ill-posed problems investigated in Gevrey classes. |
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