6 problems

Generic heat-control conjecture. Generically with respect to the lengths $(\ell_i)_{i=1,\dots,N}$, the heat equation is small-time null-controllable.

Let $T_M$ be the minimal time for uniform controllability, defined by … Let $T_0$ denote the optimal time required for every relevant trajectory of the transport field to reach the…

Regularity-gap conjecture. Not every initial condition in $H^1({\mathbb T})\times L^2({\mathbb T})$ can be steered to $0$ in time $T$ with $L^2$ controls.

Let $H^s_{k,m}$ be the fractional anisotropic Shubin operator, let $g L^2(\mathbb R^n)$, and let $c_1,c_2>0$. Write $\mu_{s,k,m}$ and $\nu_{s,k,m}$ for the GelfandShilov indices as…

Consider the degenerate parabolic equation on $(-1,1)$ with degeneracy parameter $\alpha\in[0,1)$, an interior control supported on $(a,b)$ with $0<a<b<1$, and null controllability…

Let $\alpha$ be the parameter in the systems considered in the paper, and suppose that the associated systems, including the heat and Schrödinger models, are null controllable when…