5 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…

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.

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…