| Abstract: |
| n this talk, we investigate the small-time controllability of a class of nonlinear parabolic evolution equations posed on a torus of arbitrary dimension and driven by bilinear control terms. Assuming an appropriate saturation condition on the potential, we prove a small-time approximate controllability result between states that share the same sign. In the one-dimensional setting, this result can be strengthened by coupling it with a local exact controllability property. This combined approach yields small-time exact controllability from any positive initial state to the ground state of the associated evolution operator. |
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