Control of degenerate parabolic equations of hypoelliptic type

For evolution equations associated with hypoelliptic operators, control properties are less understood than for uniformly parabolic equations. Recent studies proved that a few results from the uniformly parabolic case still hold in hypoelliptic setting, but new behaviors also appear : a positive minimal time and/or a geometric control condition can be required for the null controllability.

This talk will present the state of the art on this topic, focusing on Grushin type operators, Heisenberg and Kolmogorov operators.