6 problems

Fix $M>0$. Let $\eta\in(0,1)$ and $m\in\mathbb{Z}$. Let $J_2,J_3\geq J_1\geq J_{\mathrm{min}}\geq 1$, and let $C=C(m,M,J_1,J_2,J_3,\eta)>0$. For any $|a|\leq M$ and any solution…

Let $E(t)$ denote the beam's energy, let $\alpha$ be the fractional derivative order, and let $\eta$ be the associated parameter. Conjecture. For $\alpha=0.5$ (or similar values) a…

Let $E(t)$ denote the energy, let $\gamma$ be the time-dependent damping coefficient, and let $m>5$. Suppose that there exists a function $kappa(t)$ satisfying suitable conditions.…

The paper considers lower estimates for the energy decay of the nonlinearly damped Timoshenko system with thermoelasticity. Optimality conjecture. Driving these lower estimates sho…

Let $\psi$ be a solution of the scalar wave equation on a Kerr-AdS black-hole exterior, and let the logarithmic decay estimate be denoted by … is sharp. This conjecture is motivate…

Consider a semilinear wave equation in two space dimensions whose cubic homogeneous part is denoted by $F^{(c)}$, and write $boldsymbol{theta}=(-1,boldsymbol{ u})$ with…