11 problems

Let the fire propagate with unit speed in all directions from $R_0=B_1(0)$, and let the barrier be constructed at constant speed $\sigma>0$, so that $F=\overline{B_1(0)}$ and…

Let $r$ denote the parameter in the spherical Dubins vehicle problem, and let $C$ denote a circular path segment. For $r > \frac{1}{2}$, the candidate list of paths may contain mor…

Generic wave control conjecture. Generically with respect to the lengths $(\ell_i)_{i=1,\dots,N}$, (GGCC) is a necessary and sufficient condition for the internal control of the wa…

Generic Schrödinger control conjecture. Generically with respect to the lengths $(\ell_i)_{i=1,\dots,N}$, (GGCC) is a necessary and sufficient condition for the internal control of…

Avdonin–Zhao's watershed conjecture. The watershed description of Avdonin and Zhao provides the optimal time for the observation and control of the free wave equation on a graph.

Optimality conjecture. The above eradication strategy is optimal for the minimum time problem.

Symmetry–flatness conjecture. Symmetry plays a role in differential flatness.

Generalized geometric condition conjecture. Uniform stabilization holds if and only if the generalized geometric condition holds.

Let $\boldsymbol{\Sigma}$ be a compact interior hypersurface of a Riemannian manifold $(M,g)$. Let $\Delta_\Sigma$ be the Laplace–Beltrami operator induced on $\Sigma$, and define…

Let $(M,g)$ be a Riemannian manifold and let $\boldsymbol{\Sigma}$ be an interior hypersurface with positive definite second fundamental form satisfying the transversal geometric c…

Stable-trajectory conjecture. The good condition for observability and controllability is that $\omega$ meets all stable trajectories.