Null-controllability of non-autonomous Ornstein-Uhlenbeck equations

TL;DR

This paper proves the null-controllability of non-autonomous Ornstein-Uhlenbeck parabolic equations under a Kalman condition, demonstrating a Gevrey regularizing effect that enables control from certain regions.

Contribution

It establishes null-controllability for these equations using a Gevrey regularization and adapts the Lebeau-Robbiano method, extending control results beyond classical heat equations.

Findings

Null-controllability holds for the equations when a Kalman condition is satisfied.

The equations exhibit a Gevrey regularizing effect at positive times.

Control is achievable from regions where null-controllability is known for heat equations.

Abstract

We study the null-controllability of parabolic equations associated to non-autonomous Ornstein-Uhlenbeck operators. When a Kalman type condition holds for some positive time $T>0$, these parabolic equations are shown to enjoy a Gevrey regularizing effect at time $T>0$. Thanks to this regularizing effect, we prove by adapting the Lebeau-Robbiano method that these parabolic equations are null-controllable in time greater than or equal to $T>0$ from control regions, for which null-controllability is classically known to hold in the case of the heat equation.