8 problems

Qualitative similarity conjecture. The optimal weight $\widehat p$ is qualitatively very similar to $p^*$.

Monotonicity conjecture. For any $\beta>1$, the map

Let $f=f_B$, and let $k$ be sufficiently large depending on the internal parameters $Omega$, $L$, $b$, and $p$. There is a proper fractal exponential attractor … with finite fract…

The nonlinear plate dynamics has a fractal exponential attractor constructed in the preceding analysis. Smoothness conjecture. The fractal exponential attractor is in fact smooth.…

Simple angular dependence conjecture. The fundamental modes of $\mathbb{B}(R)$ can be written as linear combinations of $u_1(r,\hat{\theta})$.

Free-plate isoperimetric conjecture. One has

Let $\overline{e}_1$ be the positive least eigenfunction of the relevant plate operator, normalized in $H_*^2(\Omega)$, and let $u$ denote the nontrivial stable equilibrium in the…

Let $\Omega$ be the bridge domain, let $f=0$ be the absence of external load, and let $\lambda_1$ be the least eigenvalue. Define … where $\overline{e}_1$ is the positive least eig…